" 


ELECTROLYTIC  DISSOCIATION 


THE  THEORY 


OF 


ELECTROLYTIC  DISSOCIATION 


AND 


SOME    OF    ITS    APPLICATIONS 


BY 


HARRY   C.   JONES 

PROFESSOR    OF   PHYSICAL    CHEMISTRY   IN   THE 
JOHNS   HOPKINS   UNIVERSITY 


THIRD    EDITION 


THE    MACMILLAN    COMPANY 

LONDON :   MACMILLAN  &  CO.,  LTD. 
1906 

All  rights  reserved 


COPYRIGHT,  1900, 
BY  THE  M  ACM  ILL  AN   COMPANY. 


Set  up  and  electrotyped.     Published  January,  1900.     Reprinted 
June,  1904  ;  November,  1906. 


Norton  on  Iprrss 

J.  S.  Cashing  &  Co.  —  Berwick  &  Smith  Co. 
Norwood,  Mass.,  U.S.A. 


PREFACE   TO   THE   THIRD   EDITION 

AT  the  time  when  this  book  first  appeared  in  1900,  the 
Theory  of  Electrolytic  Dissociation  was  recognized  by 
physical  chemists  to  be  a  well-established  and  fundamental 
generalization.  They  regarded  it  not  only  as  one  of  the 
three  or  four  generalizations  upon  which  the  new  physical 
chemistry  rests,  but  as  being  of  scarcely  less  importance 
for  the  whole  subject  of  general  inorganic  chemistry. 

At  that  time  the  wide-reaching  significance  of  this 
theory  for  general  chemistry  was  not  fully  appreciated 
by  those  who  have  to  teach  this  subject. 

In  the  last  few  years  a  marked  change  has  come  about. 
The  Theory  of  Electrolytic  Dissociation  has  found  its  way 
not  only  into  the  teaching  of  advanced  inorganic  chemis- 
try, but  is  now  introduced  by  the  progressive  teachers  into 
their  elementary  courses.  This  change  has  been  brought 
about  largely  by  the  recognition  of  the  fact  that  this 
generalization  correlates  great  masses  of  facts  which  hith- 
erto have  been  regarded  as  more  or  less  disconnected,  and 
thus  an  important  step  is  taken  towards  placing  chemistry 
on  the  basis  of  an  exact  science. 

The  recognition  of  the  fact  that  it  is  the  charged  parts 
or  ions,  and  not  the  uncharged  atoms  or  molecules  that 
are  the  chemically  active  agents,  has  changed,  funda- 
mentally, the  teaching  and  study  of  general  chemistry. 

The  next  few  years  will  probably  see  a  still  more  general 
adoption  of  the  newer  conceptions. 


238898 


PREFACE   TO    SECOND    EDITION 

WHEN  this  little  volume  was  first  written,  the  Theory 
of  Electrolytic  Dissociation  was  well  established,  but  was 
much  less  known  than  at  present.  During  the  past  few 
years  it  has  become  the  household  word  of  practically 
every  scientific  chemist,  and  is  now  recognized  to  be 
indispensable  to  the  development  of  chemical  science. 
Indeed,  it  has  become  of  such  fundamental  importance 
that  it  is  now  introduced  into  the  very  early  stages  of 
the  teaching  of  chemistry,  and  the  chemistry  of  atoms 
and  molecules  is  rapidly  giving  place  to  the  chemistry 
of  ions. 

The  Theory  of  Electrolytic  Dissociation  has  thus  ac- 
quired a  new  interest,  and  will  doubtless  ingraft  itself 
more  and  more  deeply  into  general  chemistry. 

A  number  of  minor  changes  have  been  made,  but  the 
plan  of  the  second  edition  of  this  book  is  essentially  the 
same  as  the  first;  the  reception  with  which  the  work 
has  met  having  led  to  the  conviction  that  serious  changes 
might  injure  rather  than  improve  the  work. 

H.  C.  J. 


PREFACE 

DURING  the  last  few  years  the  writer  has  been  frequently 
asked,  directly  and  by  letter :  Where  can  an  account  of  the 
newer  developments  in  physical  chemistry  be  obtained  ? 
Where  can  we  learn  something  about  the  relation  between 
osmotic  pressure  and  gas  pressure,  and  about  the  origin 
and  significance  of  the  theory  of  electrolytic  dissociation  ? 
The  most  satisfactory  reply  which  could  be  made  was, 
read  certain  original  papers.  But  these  were  not  always 
accessible,  and,  in  some  cases,  not  quite  adapted  to  the 
state  of  development  of  the  reader.  While  it  is  true  that 
certain  chapters  in  some  of  the  text-books  on  physical 
chemistry  are  helpful  in  the  direction  indicated,  yet  no 
one  of  them  seemed  to  meet  entirely  the  demands  of  a 
large  number  of  students. 

This  little  volume  has  been  written  with  the  hope  of 
supplying  students  of  chemistry,  physics,  and  physical 
chemistry  with  at  least  a  part  of  the  information  which 
they  desire.  It  aims  to  give  an  account  of  the  origin  and 
significance  of  these  newer  developments.  A  student 
who  has  a  fair  knowledge  of  the  origin  of  the  theory  of 
electrolytic  dissociation,  of  the  evidence  upon  which  it 
rests,  and  of  its  applications,  has  already  acquired  an  ele- 
mentary conception  of  many  of  the  fundamental  principles 
which  underlie  modern  physical  chemistry. 

In  order  that  the  relation  between  the  newer  and  the 
older  physical  chemistry  may  be  the  better  understood,  a 


VI  PREFACE 

chapter  is  devoted  to  the  latter.  A  few  typical  pieces 
of  work  in  the  earlier  period  are  considered  very  briefly, 
and  some  of  the  conclusions  reached  are  pointed  out.  It 
is  hoped,  in  this  way,  to  show  clearly  the  nature  of  the 
problems  solved,  the  methods  employed,  and  some  of  the 
results  obtained. 

The  origin  and  development  of  the  theory  are  then  taken 
up.  This  is  followed  by  an  examination  of  some  of  the 
more  important  lines  of  evidence  bearing  upon  the  theory ; 
and,  finally,  some  applications  of  the  theory  in  chemistry, 
physics,  and  biology  are  considered. 

The  attempt  is  made  to  answer,  in  part,  the  questions : 
What  was  physical  chemistry  before  the  theory  of  electro- 
lytic dissociation  arose  ?  How  did  the  theory  arise  ?  Is  it 
true  ?  What  is  its  scientific  use  ? 

It  is  believed  that  a  closer  acquaintance  with  the  facts 
will  but  serve  to  increase  the  interest  in  physical  chemistry, 
which  is  already  manifesting  itself  in  so  many  directions. 

I  wish  to  express  my  indebtedness  to  my  friend  Dr.  S. 
H.  King,  for  valuable  assistance  in  reading  the  proof  of 
this  volume. 

HARRY  C.  JONES. 

JOHNS  HOPKINS  UNIVERSITY, 
October,  1899. 


CONTENTS 

CHAPTER   I 

THE  EARLIER  PHYSICAL   CHEMISTRY 

PAGE 

RELATIONS    BETWEEN    PROPERTIES    AND    COMPOSITION,    AND 

PROPERTIES  AND  CONSTITUTION i 

Introduction I 

The  Boiling-Points  of  Liquids 4 

Specific  Heat  of  Liquids         .......  8 

Atomic  and  Molecular  Volumes     .         .         .         .         .         .11 

Viscosity 14 

Refraction  of  Light 16 

Rotation  of  the  Plane  of  Polarization 21 

Magnetic  Rotation  of  the  Plane  of  Polarization      ...  27 

Conclusion  from  the  Preceding  Work 29 

The  Study  of  Solutions 30 

Other  Lines  of  Work 31 

THE  DEVELOPMENT  OF  THERMOCHEMISTRY      ....  32 

Work  of  Hess 32 

Favre  and  Silbermann  ........  33 

Work  of  Berthelot 34 

Work  of  Julius  Thomsen -35 

Thermochemical  Results .36 

THE  DEVELOPMENT  OF  ELECTROCHEMISTRY  39 

Davy's  Electrochemical  Theory 40 

Berzelius's  Electrochemical  Theory 40 

Faraday's  Law 44 

Electrolysis 45 

Theories  of  Electrolysis         .......  46 

Clausius's  Theory  of  Electrolysis 48 

vii 


Vlll  CONTENTS 

PAGE 

Williamson's  Theory  of  Electrolysis 50 

Hittorf ' s  Work  on  the  Migration  Velocity  of  Ions          .         .  52 

Kohlrausch's  Work  on  the  Conductivity  of  Solutions     .         .  52 

THE  DEVELOPMENT  OF  CHEMICAL  DYNAMICS  AND  CHEMICAL 

STATICS 53 

Wilhelmy's  Discovery  of  the  Law  of  Reaction  Velocity           .  56 

Work  of  Berthelot  and  Pean  de  St.  Gilles      ....  58 

Guldberg  and  Waage's  Law  of  Mass  Action           ...  60 

The  Application  of  Thermodynamics  to  Chemical  Processes  64 

Methods  of  Measuring  Affinity 67 

Conclusions  from  the  Earlier  Physical  Chemical  Work  .         .  68 


CHAPTER   II 

THE   ORIGIN  OF  THE    THEORY  OF  ELECTROLYTIC 
DISSOCIA  TION 

PFEFFER'S  OSMOTIC  INVESTIGATIONS 71 

Introduction 71 

PfefFer's  Method  of  Measuring  Osmotic  Pressure   .        .  72 

Some  of  Pfeffer's  Results       . 75 

RELATIONS  BETWEEN  OSMOTIC  PRESSURE  AND  GAS  PRESSURE 

DISCOVERED   BY   VAN'T   HOFF 76 

Historical .".'•'•  .76 

Boyle's  Law  for  Dilute  Solutions  .  .  .  *  .  .82 

Gay  Lussac's  Law  for  Dilute  Solutions 84 

Experimental  Evidence  in  Favor  of  both  the  Laws  of  Boyle 

and  Gay  Lussac  for  Solutions 85 

Avogadro's  Law  for  Dilute  Solutions 87 

General  Expression  of  the  Laws  of  Boyle,  Gay  Lussac,  and 

Avogadro  for  Solutions  and  Gases  .....  89 
Exceptions  to  the  General  Applicability  of  the  Gas  Laws  to 

Osmotic  Pressure 91 

ON  THE  DISSOCIATION  OF  SUBSTANCES  DISSOLVED  IN  WATER. 

BY  SVANTE  ARRHENIUS 93 

Summary 101 


CONTENTS  ix 


CHAPTER   III 

EVIDENCE  BEARING    UPON  THE   THEORY  OF  ELEC- 
TROLYTIC DISSOCIATION 

PAGE 

THE   PHYSICAL    PROPERTIES    OF    COMPLETELY    DISSOCIATED 

SOLUTIONS  SHOULD  BE  ADDITIVE 104 

Specific  Gravity  of  Salt  Solutions '    105 

Change  of  Volume  in  Neutralization  .  .  .  .  .  107 
Specific  Refractive  Power  of  Salt  Solutions  ....  108 
Rotatory  Power  of  Salt  Solutions  .  .  .  .  .no 

The  Color  of  Salt  Solutions no 

A  Demonstration  of  the  Dissociating  Action  of  Water  .  .113 
Conductivity  is  Additive.  The  Law  of  Kohlrausch  .  .116 

PROPERTIES  OF  COMPLETELY  DISSOCIATED  AND  OF  UNDISSO- 

CIATED  MIXTURES 117 

Mixtures  of  Two  Completely  Dissociated  Compounds  .  .117 
Mixtures  of  Two  Completely  Undissociated  Compounds  .  118 

HEAT  OF  NEUTRALIZATION  IN  DILUTE  SOLUTIONS   .        .        .119 
Strong  Acids  and  Bases         .         .         .         .         .         .         .121 

Weak  Acids  and  Strong  Base 121 

Hess's  Law  of  the  Thermoneutrality  of  Salt  Solutions    .        .122 

OSMOTIC  PRESSURE  —  LOWERING  OF  FREEZING-POINT  —  RISE 

IN  BOILING-POINT  —  CONDUCTIVITY  .  .  .  .123 

Relation  between  Osmotic  Pressure  and  Lowering  of  Freezing- 
point  126 

Relation  between  Osmotic  Pressure  and  Lowering  of  Vapor- 
tension.  Rise  in  Boiling-point 127 

Relation  between  Osmotic  Pressure  and  Conductivity    .         .128 

Relation  between  Lowering  of  Freezing-point  and  Rise  in 
Boiling-point 129 

Relation  between  Lowering  of  Freezing-point  and  Conductivity     1 29 

Connection  between  Osmotic  Pressure  and  Lowering  of  Freez- 
ing-point, established  by  Thermodynamics  .  .  .131 

Relation  between  Osmotic  Pressure  and  Lowering  of  Vapor- 
tension  (Rise  in  Boiling-point).  Theoretical  Demon- 
stration   134 


X  CONTENTS 

PAGE 

EXPERIMENT  TO  SHOW  THE  PRESENCE  OF  FREE  IONS      .        .137 
Illustration  of  a  Solution  charged  Electrostatically         .         .138 

Experiment  of  Ostwald  and  Nernst 139 

The  Ostwald  Dilution  Law 142 

Ostwald's  Deduction 143 

Rudolphi's  Dilution  Law        .......     147 

EFFECT  OF  AN  EXCESS  OF  ONE  OF  THE  PRODUCTS  OF  DISSO- 
CIATION   '.-  .  149 

Further  Relation  between  Dissociation  by  Heat  and  Electro- 
lytic Dissociation 149 

Determination  of  Electrolytic  Dissociation  by  Change  in 
Solubility 151 

Agreement  between  Dissociation  determined  by  Conductivity, 
Freezing-point  Lowering,  and  Solubility  .  .  .  .152 

The  Relation  between  the  Two  Kinds  of  Dissociation  an 
Analogy  .  .  .  - .,.  .  153 

DISSOCIATION  AND  CHEMICAL  ACTIVITY 154 

Conductivity  and  Reaction  Velocity       .         .         .        ,        .155 
Dissociation  measured  by  Chemical  Activity  .         .         .157 

Chemical  Reactions  usually  take  Place  between  Ions    .:,  .      .     158 
Dissociating  Power  of  Different  Solvents       .         .        ,.         .160 

EFFECT  OF  WATER  ON  CHEMICAL  ACTIVITY    .        .        ...       .  160 

Action  of  Dry  Chlorine  on  Metals          .         .         .         .,      ,.  161 

Comparative  Inactivity  of  Dry  Oxygen           .        ,.        .         .  162 

Dry  Hydrochloric  Acid  does  not  decompose  Carbonates        .  163 

Dry  Acids  exert  no  Action  on  Litmus  and  do  not  form  Salts  165 
Dry  Hydrochloric  Acid  does  not  precipitate  Silver  Nitrate  in 

Ether  or  Benzene 165 

Comparative  Inactivity  of  Dry  Hydrogen  Sulphide         .         .  165 

Other  Reactions  which  do  not  take  Place  without  Water        .  168 
Dry  Hydrochloric  Acid  does  not  act  on  Dry  Ammonia  .         .168 

Dry. Sulphuric  Acid  does  not  act  on  Dry  Metallic  Sodium      .  169 

Conclusion 170 


CONTENTS  xi 


CHAPTER   IV 

SOME  APPLICATIONS  OF  THE    THEORY  OF  ELECTRO- 
LYTIC DISSOCIATION 

PAGE 

APPLICATION  OF  THE  THEORY  OF   ELECTROLYTIC  DISSOCIA- 
TION TO  CHEMICAL  PROBLEMS 171 

THE  THEORY  OF  ELECTROLYTIC  DISSOCIATION  AS  APPLIED  TO 

SOLUTIONS 172 

Osmotic  Pressure  .        .        » 173 

Diffusion 174 

Lowering  of  Freezing-point 176 

Lowering  of  Vapor-tension,  Rise  in  Boiling-point  .         .         .178 
The  Theory  of  Electrolytic  Dissociation  as  applied  to  Electro- 
chemistry .         .         . 182 

Electrolysis .        .183 

Modes  of  Ion  Formation 189 

Velocity  of  Ions     .         .         .         .         .         .         .         .         .     191 

Relative  Velocity  of  Ions 192 

Kohlrausch's  Law  of  the  Independent  Migration  Velocity  of 

Ions 197 

The  Absolute  Velocity  of  Ions .198 

The  Conductivity  of  Solutions 201 

Specific  Conductivity     .         .         .         .         .         .  .     202 

Method  of  Measuring  the  Conductivity  of  Solutions       .         .     203 
Carrying  out  a  Conductivity  Measurement     ....     206 

Conductivity  of  Water 207 

Calculation  of  Dissociation 209 

The  Conductivity  of  Solutions  in  the  Different  Solvents  varies 

very  greatly 211 

Thomson's  Theory        .         .         .         .         .         .         .         .213 

Conductivity  at  Elevated  Temperatures          .        .         .        .215 

Electromotive  Force 216 

Strength  of  Acids  and  Bases 216 

Relations  between  Acidity  and  Composition  and  Constitution     219 
Bases 223 

APPLICATION  -  OF  THE  THEORY  OF    ELECTROLYTIC  DISSOCIA- 
TION TO  A  PHYSICAL  PROBLEM  .        .     226 


xii  CONTENTS 

PAGS 

THE  SEAT  OF  THE  ELECTROMOTIVE  FORCE  IN  PRIMARY  CELLS  226 

Calculation  of  Electromotive  Force  from  Osmotic  Pressure    .  227 

Electrolytic  Solution-tension       '  .         .      -.     -  .         ..       .  231 

Constancy  of  Solution-tension 236 

Calculation  of  the  Difference  in  Potential  between  Metal  and 

Solution .         .        .         .  237 

Types  of  Cells 238 

Concentration  Elements  of  the  First  Type     ....  239 

Concentration  Elements  of  the  Second  Type          .         .         .  243 

Liquid  Elements 247 

Theory  of  the  Liquid  Element       ......  247 

Sources  of  Potential  in  a  Concentration  Element  .         .         .252 

The  Electromotive  Force  of  the  Daniell  Element  .         .         .  254 

The  Gas-battery   .         .         .         ...         .         .         .  256 

Chemical  Action  at  a  Distance 261 

Experiment  to  demonstrate  Chemical  Action  at  a  Distance    .  262 

Conclusion    .         .         .         .         .         .  -.         .         .  267 

APPLICATION  OF  THE  THEORY  OF   ELECTROLYTIC   DISSOCIA- 
TION TO  BIOLOGICAL  PROBLEMS 268 

Toxic  Action  and  Electrolytic  Dissociation    ....  268 

Toxic  Action  of  the  Phenols  and  their  Dissociation       .         .  272 

Dissociation  and  Disinfecting  Action     .....  273 

Toxic  Action  of  Substances  on  Certain  Fungi        .        .         .  275 

Application  of  the  Dissociation  Theory  to  Animal  Physiology  276 

Physical  Chemical  Methods  applied  to  Animal  Physiology     .  278 
Application  of  Osmotic  Pressure  and  Dissociation  to  the 

Mechanics  of  Secretion 281 

Conclusion    .  ...  282 


ELECTROLYTIC  DISSOCIATION 


ELECTROLYTIC    DISSOCIATION 
CHAPTER   I 

THE  EARLIER  PHYSICAL  CHEMISTRY 

RELATIONS    BETWEEN    PROPERTIES    AND    COMPOSITION,    AND 
PROPERTIES    AND    CONSTITUTION 

Introduction.  —  Such  marked  advances  have  been  made 
in  physical  chemistry  during  the  last  few  years,  that  it 
is  sometimes  thought  that  this  is  distinctively  a  new  branch 
of  science.  Indeed,  the  beginning  of  physical  chemistry 
is  often  regarded  as  contemporaneous  with  the  origin  of 
the  theory  of  electrolytic  dissociation. 

While  it  is  true  that  the  new  physical  chemistry,  which 
has  revolutionized  so  many  of  our  chemical  conceptions, 
has  grown  up  around  the  theory  of  electrolytic  dissocia- 
tion, nevertheless,  we  must  not  forget  that  the  newer  is 
built  upon,  and  incorporates,  the  entire  work  of  the  cen- 
tury. Indeed,  the  theory  of  electrolytic  dissociation  itself 
had  its  beginning,  as  we  shall  see,  about  the  middle  of  the 
century. 

What  was  termed  physical  chemistry,  prior  to  1885,  was 
largely  a  study  of  the  physical  properties  of  chemical 
substances,  and  work  of  this  kind  is  in  progress  up  to 
the  present.  At  first,  the  physical  properties  of  the  ele- 


2  ELECTROLYTIC  DISSOCIATION 

ments,  and  of  compounds,  attracted  attention,  with  the 
result,  that  the  laws  of  gases,  liquids,  and  solids  were  dis- 
covered. The  earlier  workers  in  this  field,  however,  were 
not  content  with  a  disjointed  knowledge  of  the  properties 
of  substances ;  they  began  to  look  for,  and  discover,  rela- 
tions ;  for  the  highest  aim  of  scientific  investigation  is  to 
find  out  relations  between  apparently  disconnected  facts  — 
to  discover  generalizations.  The  first  point  which  would 
naturally  be  taken  up  was  the  relation  between  properties 
and  chemical  composition.  How  would  the  introduction 
of  an  oxygen  or  a  chlorine  atom  into  a  compound  affect 
the  physical  properties  of  the  compound ;  or  the  intro- 
duction of  a  CH2  group  into  organic  compounds  alter 
their  properties?  The  study  of  this  relation  was  com- 
paratively simple.  It  was  only  necessary  to  prepare 
a  compound,  study  its  properties,  then  introduce  an 
oxygen  or  chlorine  atom,  or  a  CH2  group,  and  study  the 
properties  of  the  new  compound  formed.  By  applying 
this  process  to  a  large  number  of  substances,  relations 
between  composition  and  properties  could  be  discovered, 
and  much  valuable  work  was  done  along  this  line. 

But  it  was  well  known  that  there  are  many  chemical 
compounds  which  have  the  same  composition,  but  very 
different  physical  properties.  Isomeric  substances  in  gen- 
eral have  different  physical  properties.  Isomeric  sub- 
stances have  the  same  kind  of  atoms  in  the  molecule ;  but 
there  is  the  possibility  that  the  molecule  of  one  isomeric 
substance  may  be  the  simplest  possible,  and  the  molecule 
of  the  other  isomeric  substance  may  be  an  aggregate  of 
the  simplest  molecules;  and  this  might  account  for  the 
difference  in  properties  of  isomeric  substances. 


THE  EARLIER  PHYSICAL  CHEMISTRY  3 

There  are  also  other  substances,  called  metameric,  which 
have  not  only  the  same  kind  of  atoms  in  the  molecule,  but 
the  same  number  of  the  same  kind  of  atoms ;  and  yet 
have  different  physical  properties. 

The  composition  of  the  molecules  in  the  two  cases  is 
exactly  the  same,  so  that  the  difference  in  properties,  in 
such  cases,  cannot  be  attributed  to  a  difference  either  in 
the  kind  or  number  of  atoms  in  the  molecule.  To  what 
then  is  the  difference  in  properties  in  such  cases  to  be 
attributed  ?  If  it  is  due  neither  to  the  kind,  nor  to  the 
number  of  atoms  in  the  molecule,  it  must  be  due  to  the 
way  in  which  the  atoms  are  combined  with  one  another  in 
the  molecule.  This  brings  us  to  the  second  problem 
which  was  investigated  by  the  earlier  physical  chemists, 
the  relation  between  properties  and  constitution. 

In  investigating  this  point,  such  questions  arose  as  what 
would  be  the  effect  on  the  physical  properties,  produced 
by  oxygen  in  the  carbonyl  condition  (CO),  with  respect  to 
oxygen  in  the  hydroxyl  condition  (OH)?  Or  how  would 

/C\ 
carbon  atoms  combined  as  in  ethylene  f  II  J  differ  in  their 

effect  on  the  physical  properties  of  the  compound,  from 

/C\ 

carbon   atoms   combined   as   in   ethane  (  I  J?     By   using 

metameric  compounds  such  questions  could  be,  and  in  a 
number  of  cases  have  been,  answered. 

Work  of  this  earlier  kind  had  to  do  with  gases,  liquids, 
and  solids,  but  we  will  confine  ourselves  to  that  which 
has  been  done  upon  liquids ;  since  relations  have  been 
more  fully  developed  here  than  for  either  gases  or 
solids. 


4  ELECTROLYTIC   DISSOCIATION 

The  Boiling-points  of  Liquids.  —  A  relation  between  the 
boiling-points  of  liquids  and  their  composition  was  first 
pointed  out  by  Kopp,1  in  1842.  An  elaborate  investigation 
on  the  boiling-points  of  a  large  number  of  organic  com- 
pounds was  published  in  i855,2  the  result  of  which  was  to 
show  that  his  earlier  generalization  was,  in  the  main,  cor- 
rect. The  following  are  a  few  of  the  data  obtained  by 
Kopp,  and  these  will  suffice  to  bring  out  the  relation  be- 
tween composition  and  boiling-point  discovered  by  him  :  — 

SUBSTANCE  BOILING-POINT 

Methyl  alcohol,     CH4O  65 


Ethyl  alcohol,        C2H6O  78' 

\i8c 
Propyl  alcohol,      C3H8O  96°' 

Butyl  alcohol,         C4H10O  109 

Amyl  alcohol,         C5H12O  132' 

Ethyl  formate,       C3H6O2  55\ 

X19' 

Ethyl  acetate,        C4H8O2  74°( 

>22< 

Ethyl  propionate,  C5H10O2  96°' 

Formic   acid,        CH2O2  IO5°\ 

Acetic  acid,  C2H4O2  117 

Propionic  acid,      C3H6O2  142 

Butyric  acid,          C4H8O2  156 

>20° 

Valeric  acid,          C5H10O2  176°^ 

1  Liebig's  Ann.,  41,  86,  169  (1842).  2  ibid.,  96,  i  (1858). 


THE   EARLIER   PHYSICAL   CHEMISTRY  5 

Take  succeeding  members  of  any  of  the  above  three 
groups  of  compounds ;  they  differ  in  composition  by  one 
carbon  atom  and  two  hydrogen  atoms, — by  the  group  CH2, 
—  and  there  is,  in  every  case,  an  approximately  constant  dif- 
ference between  the  boiling-points  of  succeeding  members. 
This  relation  between  composition  and  boiling-point,  Kopp 
formulated  from  data  obtained  much  earlier,  as  follows  : 
Equal  differences  in  the  chemical  composition  of  organic 
compounds  correspond  to  equal  differences  in  the  boiling- 
points. 

It  is  obvious  from  the  above  data  that  this  relation  holds 
only  approximately. 

If  the  above  relation  held  rigidly,  then  isomeric  sub- 
stances having  the  same  composition  must  have  the  same 
boiling-point.  The  following  data  will  serve,  in  part,  to 
show  the  validity  of  this  conclusion  :  — 

SUBSTANCE  BOILING-POINT 

r  Methyl  acetate  56° 

I  Ethyl  formate  55° 

|  Methyl  butyrate  95° 

{  Ethyl  propionate  96° 


Methyl  valerate  II5° 

Amyl  formate  116° 

Ethyl  butyrate  115° 

We  might  conclude  from  the  above  data,  that  isomeric 
compounds  have  the  same,  or  very  nearly  the  same,  boiling- 
point.  It  should  be  observed,  however,  that  the  above 
isomeric  compounds  have  similar  constitution.  As  soon  as 
isomeric  compounds  which  have  different  constitution 


6  ELECTROLYTIC  DISSOCIATION 

were  compared,  it  was  found  that  they  have  very  different 
boiling-points;  which  shows  that  boiling-point  is  con- 
ditioned not  simply  by  the  number  and  kind  of  atoms 
in  the  molecule,  but  also  by  the  way  in  which  these  atoms 
are  combined  with  one  another. 

Subsequent  work  has  shown  that  these  relations, 
pointed  out  by  Kopp,  are  only  rough  approximations. 
Dittmar1  has  proved  that  metameric  compounds,  such  as 
methyl  acetate  and  ethyl  formate,  do  not  have  the  same 
boiling-point,  and  more  accurate  work  on  the  boiling- 
points  of  homologous  series  of  compounds  has  shown  that 
the  difference  between  the  boiling-points  of  succeeding 
members  is  not  constant,  but  usually  decreases  as  the  com- 
pounds become  more  complex.  This  is  illustrated  by  the 
following  data,  taken  from  the  work  of  Schorlemmer : 2  — 

SUBSTANCE  BOILING-POINT 

C4H10  i° 

>37° 
C5H12  380< 

v 

C6H14  7o°X 

C7H16  99' 

C8H18  125' 

C2H5C1  12.5 

C3H7C1  46.4 

C4H9C1  77-6' 

>8.0° 

C5HnCl  I05.60/ 

1  Liebig's  Ann.  Suppl.,  6,  313  (1868).  «  Liebig's  Ann.,  161,  281. 


THE   EARLIER   PHYSICAL  CHEMISTRY 
SUBSTANCE  BOILING-POINT 

C2H5Br  39.0 


C3H7Br 

•4 
C4H9Br  100.4' 


C5HuBr  128.7' 

Some  interesting  facts  in  connection  with  the  relation  be- 
tween constitution  and  boiling-point  have  been  discovered. 
Take  the  benzene  hydrocarbons,  and  compare  those  in 
which  one  hydrogen  has  been  replaced  by  a  group,  with 
those  having  two  hydrogen  atoms  replaced ;  and  these,  in 
turn,  with  those  having  three  hydrogen  atoms  replaced. 

COMPOUNDS  WITH  ONE 
HYDROGEN  ATOM  REPLACED  BOILING-POINT 

C6H5C2H5  134° 

C6H5C3H7  152° 

C6H5C4H9  ( 1 72°  calculated) 

C6H5C5Hn  193° 

COMPOUNDS  WITH  Two 
HYDROGEN  ATOMS  REPLACED  BOILING-POINT 


C6H4(CH3)2 

XCH8 
C6H/  159-160° 


/CH3 
C6H/  I7S-I780 

\£   TT 

C6H4(C2H5)72  178-179° 

COMPOUNDS  WITH  THREE 
HYDROGEN  ATOMS  REPLACED  BOILING-POINT 

C6H3(CH3)3  165-166° 

/(CH3), 
C6H/  183-184° 

\CH 


-i 
8  ELECTROLYTIC   DISSOCIATION 

By  comparing  these  three  classes  of  substances,  we  see 
that  the  second  boils  higher  than  the  first,  and  the  third 
higher  than  the  second.  Between  the  first  and  second 
there  is  almost  a  constant  difference  of  about  6°,  and 
between  the  second  and  third  the  difference  is  just  about 
6°,  and  is  nearly  constant. 

The  study  of  a  number  of  classes  of  primary  and 
secondary  compounds  has  established  the  fact,  that  the 
same  difference  in  constitution  produces  approximately  the 
same  difference  in  boiling-point. 

Specific  Heat  of  Liquids.  —  The  specific  heat  of  a  liquid 
is  different  at  different  temperatures.  In  determining 
specific  heats  it  is,  therefore,  necessary  to  choose  some 
temperature  for  making  the  measurements,  in  order  that 
the  results  may  be  comparable. 

Reis 1  took  the  mean  specific  heats  between  20°  and  the 
boiling-points  of  the  substances  investigated.  That  speci- 
fic heats  may  be  comparable,  it  is  necessary  to  refer  them 
to  comparable  quantities  of  substances.  Molecular  quanti- 
ties are  taken,  and  the  molecular  heats  are  compared,  to 
bring  out  any  relations  which  might  exist.  A  few  results 
for  homologous  series  of  alcohols,  acids,  and  hydrocarbons, 
will  serve  to  bring  out  any  relation  between  composition 
and  this  property. 

SUBSTANCE  MOLECULAR  HEAT 

Methyl  alcohol,  CH4O  21.0 

/9-3 
Ethyl  alcohol,     C2H6O  30.3^ 

\I0.2 

Propyl  alcohol,  C3H8O  40.5^ 

Butyl  alcohol,     C4H10O  50. 

Amyl  alcohol,     C5H12O  60. 5' 

1  Wied.  Ann.,  13,  44-, 


THE   EARLIER  PHYSICAL  CHEMISTRY 

SUBSTANCE 

Formic  acid,  CH2O2 
Acetic  acid,  C2H4O2 
Butyric  acid,  C4H8O2 
Isovaleric  acid,  C5H10O2 

Caproic  acid,      C6H12O6 
Benzene,  C6H6 

Toluene,  C7H8 

Ethyl  benzene,    C8H10 

Mesitylene,         CgH^  56  A 

The  difference  between  the  molecular  heats  of  any  two 
members  of  a  series  is  nearly  constant.  This  difference 
corresponds  to  a  difference  in  composition  of  CH2,  in  each 
series  of  compounds ;  yet  its  value  varies  somewhat  from 
one  series  to  another. 

The  effect  of  constitution  on  molecular  heat  can  be  seen 
from  the  following  examples  of  isomeric  substances :  — 

SUBSTANCE  MOLECULAR  HEAT 

f  Propyl  aldehyde,     C3H6O  32.6 

[Acetone,  C3H6O  32.6 

J  Butyric  acid,  C4H8O2  47.4 

[  Isobutyric  acid,       C4H8O2  47.6 

f  Allyl  alcohol,  C3H6O  38.1 

I  Propyl  aldehyde,     C3H6O  32.6 

Isomeric  compounds,  having  similar  constitution,  have 
very  nearly  the  same  molecular  heats  ;  but  if  the  constitu- 


10  ELECTROLYTIC  DISSOCIATION 

tions  are  markedly  different,  as  in  the  last  example,  then 
the  molecular  heats  differ  widely  from  one  another.  This 
conclusion  has  been,  in  the  main,  confirmed  by  the  work 
of  de  Heen.1  ' 

Schiff2  found  the  further  relation  between  specific  heat 
and  composition ;  that  the  specific  heat  is  nearly  the  same 
for  large  groups  of  closely  related  substances.  If  we 
represent  the  specific  heat  at  t  degrees,  by  St>  we  have 
the  following  results  :  — 

SUBSTANCE  SPECIFIC  HEAT 

Methyl  benzoate  »S/=  0.3630  -f-  0.00075  ' 

Ethyl  benzoate  Sf=  0.3740  -f-  0.00075  ^ 

Propyl  benzoate  St  =  0.3830  -f-  0.00075  / 

Benzene  St=  0.3834  -f-  0.001043  ^ 

Toluene  St  —  0.3  834  +  0.001 043  / 

-Af-Xylene  St  =  0.3  834  +  o.oo  1 043  / 

/VXylene  Sf=  0.3834  -f  0.001043  / 

Acetic  acid  ,Sy=  0.444   -f  0.001418  / 

Propionic  acid  £/=  0.444   +  0.001418  / 

Butyric  acid  *S/=  0.444    +  0.001418  / 

This  relation  can  be  generalized  as  follows :  — 

The  specific  heat  of  homologous  compounds  is  represented 
by  the  formula  c  =•  a  +  bt,  in  which  b  always  has  the  same 
value  for  the  different  members,  and  a  often  has  the  same, 
but  sometimes  slightly  different  values  for  the  different 
members. 

Later  work  by  Schiff  3  confirmed  his  earlier  results. 
Considerable  work  has  been  done  on  the  specific  heats 

1  Essai  de  phys.  comp.,  Brussels,  1883.  2  Liebig's  Ann.,  234, 300. 

8  Ztschr.  phys.  Chem.,  i,  376. 


THE   EARLIER   PHYSICAL  CHEMISTRY  II 

of  aqueous  solutions.  That  of  Marignac1  is  to  be  espe- 
cially mentioned.  He  carried  out  an  elaborate  investiga- 
tion of  closely  related  compounds,  as  chlorides,  bromides, 
iodides,  sulphates,  nitrates,  acetates,  etc.,  with  the  object  of 
discovering  any  relations  which  might  exist.  The  molec- 
ular heats  of  solutions  of  a  number  of  substances  were 
found  to  be  the  sum  of  two  parts ;  the  one  depending  upon 
the  acid,  the  other  upon  the  base  —  they  belong  to  that 
class  of  properties  which  are  known  as  additive.  But  a 
large  number  of  substances  did  not  show  this  regularity,  so 
that  no  comprehensive  generalization-was  reached. 

Atomic  and  Molecular  Volumes.  —  Here,  again,  to  find 
relations  we  must  use  comparable  quantities  of  substances, 
and  it  is  most  convenient  to  use  molecular  quantities.  If 

g  is  the  specific  gravity,  -  is  the  specific  volume.     If  m 

g 

is  the  molecular  weight,  —  is  the  molecular  volume.     A 

g 
number  of  relations  were  pointed  out  by  Kopp.2 

For  closely  allied  compounds,  the  same  difference  in 
composition  corresponds  to  the  same  difference  in  molec- 
ular volume.  This  is  seen  from  the  following  examples  :— 

SUBSTANCE  MOLECULAR  VOLUME 

CH4O  42.1 

\20.I 

C2H6O  62.2' 

C2H40  56.5 

\20.I 

CsH.,0  77-S/ 

1  Ann.  Chim.  Phys.  [5],  8,  410.  8  Liebig's  Ann.,  41,  79;  96,  153,  303. 


12  ELECTROLYTIC  DISSOCIATION 

SUBSTANCE  MOLECULAR  VOLUME 

CH202  41.4. 

\22.3 

C2H402  63.7/ 

\2I.7 

C8H602  / 

C4H8O2  i 

The  following  generalization  was  also  reached  by  Kopp : 
When  two  atoms  of  hydrogen  are  replaced  by  one  of 
oxygen,  the  molecular  volume  is  only  slightly  changed. 
Thus:  — 

SUBSTANCE  MOLECULAR  VOLUME 

Methyl  alcohol,  CH4O  42.1 

Formic  acid,  CH2O2  41.4 

Ethyl  alcohol,  C2H6O  62.2 

Acetic  acid,  C2H4O2  63.7 

\  The  relation  between  molecular  volume  and  constitution 
was  also  worked  out.  A  few  results  for  isomeric  sub- 
stances will  serve  to  bring  out  the  conclusion  reached. 

SUBSTANCE  MOLECULAR  VOLUME 

f  Acetic  acid,         C2H4O  63.7 

{  Methyl  formate,  C2H46  63.4 

J  Methyl  valerate,  C6H12O2  149.2 

{  Ethyl  butyrate,   C6H12O2  149.3 

f  Propionic  acid,    C3H6O2  85.4 

{  Ethyl  formate,     C3H6O2  85.3 

Isomeric  liquids  have  the  same  molecular  volumes. 
Kopp   found,  also,  that  the  atomic  volumes  were  not 
constants,  independent  of  the  nature  of  the  atoms  with 


THE  EARLIER  PHYSICAL  CHEMISTRY  13 

which  any  given  atom  is  combined,  but  varied  somewhat. 
Thus,  oxygen  in  hydroxyl  has  a  different  atomic  volume 
from  oxygen  in  carbonyl.  Similarly,  carbon  and  nitrogen 
in  their  different  forms  of  combination  have  different 
atomic  volumes.  Yet  the  molecular  volumes  are,  in  gen- 
eral, approximately  the  sum  of  the  atomic  volumes. 
The  following  atomic  volumes,  - 

ATOMIC  VOLUME 
P  25.5 

As  26.4 

Sb  32.3 

Sn  40.2 

show  the  relation  which  was  pointed  out  by  Kopp,  that 
the  atomic  volumes  of  the  elements  are  nearly  multiples 
of  a  constant,  the  value  of  the  constant  lying  between 
5.1  and  5.9. 

The  more  recent  work  of  Thorpe1  has  shown  that 
isomeric  liquids,  at  their  boiling-points,  do  not  always 
have  exactly  the  same  molecular  volume,,  though  the  dif- 
ference is  not  great.  While  Schiff  found  that  isomeric 
liquids,  in  general,  have  somewhat  different  molecular  vol- 
umes, the  differences  corresponding  to  the  law,  that  the 
higher  the  boiling-point  of  the  substance  the  higher  its 
molecular  volume. 

W.  Lossen2  concluded,  from  a  number  of  pieces  of 
work  carried  out  by  his  pupils,  that  we  cannot  say,  in 
general,  that  the  molecular  volume  is  additive  —  that 
it  is  the  sum  of  the  atomic  volumes  of  its  constituents. 
The  molecular  volume  depends  not  simply  on  the  kind  of 

1  Journ.  Chem.  Soc.,  141,  327  (1880).  2  Liebig's  Ann.,  254,  42,  1889. 


14  ELECTROLYTIC  DISSOCIATION 

atoms  in  the  molecule,  but  also  on  the  way  in  which  the 
atoms  are  combined  in  the  molecule. 

It  may,  however,  be  stated,  that  while  the  molecular 
volumes  of  liquids  at  the  boiling-point,  are  not  exactly  the 
sum  of  the  constant  atomic  volumes,  yet  they  are  approxi- 
mately so;  and  molecular  volume  is  approximately  an 
additive  property. 

Viscosity.  —  Some  interesting  relations  between  the  vis- 
cosity of  liquids,  and  their  composition  and  constitution, 
have  been  recently  pointed  out  by  Thorpe  and  Rodger,1  in 
their  elaborate  investigation  along  this  line.  Although  this 
work  has  been  done  very  recently,  yet  it  is  typical  of  the 
earlier  work,  and,  therefore,  belongs  in  this  place. 

The  viscosities  were  measured  by  the  time  required  for 
a  liquid  to  flow  through  a  capillary  tube.  To  calculate 
the  viscosity  coefficient,  the  formula  of  Slotte  was  used,  — 


(\+bf)ri 

in  which  77  is  the  coefficient  of  viscosity,  in  dynes  per 
square  centimetre,  c,  &,  and  n  are  constants,  varying  with 
the  nature  of  the  liquid.  To  test  the  influence  of  com- 
position and  constitution  on  viscosity,  this  property  of 
some  seventy  liquids  was  determined  in  absolute  measure, 
at  all  temperatures  from  o°  to  the  boiling-points  of  the 
liquids. 

To  compare  viscosity  coefficients,  we  must  use  compara- 
ble temperatures,  and  we  will  use  first  the  boiling-points 
of  the  liquids.  As  we  ascend  a  homologous  series  of  com- 

1  Thorpe  and  Rodger,  Proceed.  Royal  Soc.,  1894;  Bakerian  Lecture,  Royal  Soc. 
Chem.  News,  69, 123, 135 ;  Journ.  Chem.  Soc.,  71, 360 ;  Ztschr.  phys.  Chem.,  14, 361. 


THE   EARLIER   PHYSICAL  CHEMISTRY  15 

pounds,  the  coefficient  generally  decreases ;  in  a  few  cases 
it  remains  the  same,  and  in  one  series  increases.  If  we 
compare  corresponding  compounds,  we  find  that  the  one 
with  the  highest  molecular  weight  has  the  highest  coeffi- 
cient. The  effect  of  increase  in  molecular  weight,  however, 
may  be  more  than  counterbalanced  by  constitution.  Iso- 
compounds  have,  in  general,  a  larger  coefficient  than 
normal  compounds.  The  degree  of  symmetry  of  the 
molecule  can  have  a  marked  influence  on  the  size  of  the 
coefficient. 

The  following  relations  between  the  molecular  viscosi- 
ties at  the  boiling-point,  were  established  by  Thorpe  and 
Rodger.  An  increment  of  CH2  in  compounds,  with  the 
exception  of  the  alcohols,  dibromides,  and  lowest  members 
of  the  homologous  series,  corresponds  to  an  increase  in  the 
molecular  viscosity.  The  compound  having  the  highest 
molecular  weight,  with  the  exception  of  the  compounds 
mentioned  above,  has  the  highest  molecular  viscosity. 
The  differences  in  the  molecular  viscosities,  between 
corresponding  members  of  two  correlated  series,  are 
fairly  constant 

An  attempt  was  made  to  calculate  the  viscosity  constants 
of  a  number  of  atoms  and  groups,  but  since  constitution 
comes  so  largely  into  play,  it  is  evident  that  these  con- 
stants are  only  approximations.  Yet,  the  molecular  vis- 
cosity of  forty-five  liquids,  calculated  from  these  constants, 
differs  in  few  cases  more  than  5  per  cent  from  those 
found.  There  are,  however,  many  exceptions  to  this  rule. 

The  above  relations  were  all  obtained  by  comparing  the 
viscosities  of  liquids  at  their  boiling-points.  But  another 
method  of  comparison  was  also  used. 


1 6  ELECTROLYTIC  DISSOCIATION 

The  general  shape  of  the  viscosity  curves,  toward  the 
boiling-point,  was  practically  the  same.  If  tangents  are 
drawn  to  the  curves  at  points  corresponding  to  the  boiling- 
points  of  liquids,  the  inclinations  of  the  tangents  to  the 
axis,  i.e.  the  slopes  of  the  curves,  varied  but  little.  Curves 
for  the  alcohols,  etc.,  were  an  exception. 

The  temperatures  of  equal  slope  of  curves  were  then 
taken  for  comparison.  At  this  point,  the  effect  of  tem- 
perature would  be  the  same  for  different  substances. 

It  was  found  that  at  the  temperature  of  equal  slope, 
there  were  more  definite  relations  between  the  viscosity 
coefficients  and  the  chemical  nature  of  the  compounds.  At 
this  temperature  a  CH2  group  exerts  a  positive  influence 
on  the  coefficient,  which  decreases  as  the  series  ascends. 
Exceptions  are  the  alcohols,  acids,  and  dichlorides.  Of 
corresponding  compounds,  that  with  the  highest  molecular 
weight  has  the  highest  coefficient.  Iso-compounds  invari- 
ably have  a  larger  coefficient  than  normal  compounds ; 
while  for  other  isomeric  substances  a  branching  of  the 
atomic  chain  has  an  influence  on  the  magnitude  of  the 
coefficient. 

The  molecular  viscosity  at  constant  slope  can  be  calcu- 
lated from  the  fundamental  constants  for  the  constituents, 
but  here,  again,  water  and  the  alcohols  are  exceptions. 

It  is  evident  from  the  above,  that  the  relations  found, 
thus  far,  between  viscosity  and  composition  and  consti- 
tution, are,  at  best,  only  approximately  correct,  and  apply 
only  to  a  limited  number  of  cases. 

Refraction  of  Light.  —  A  number  of  attempts  have  been 
made  to  formulate  a  relation  between  the  power  of  sub- 
stances to  refract  light  and  their  densities.  Of  these,  that 


THE   EARLIER   PHYSICAL  CHEMISTRY  17 

proposed  by  Dale  and  Gladstone1  is  probably  the  most 
general.  If  we  represent  the  index  of  refraction  by  n, 
and  the  density  by  d, 

— - —  =  constant. 
a 

They  showed  that  this  relation  holds  for  a  large  number 
of  liquids,  within  very  wide  ranges  of  temperature. 

Landolt 2  tested  this  relation  very  accurately,  for  a  small 
range  of  temperature,  and  found  almost  exactly  a  constant 
for  a  number  of  substances.  Others3  have,  however, 
obtained  results  to  which  the  above  expression  did  not 

accurately  apply,  the  value  n  ~  I  either  increasing  or  de- 
af 

creasing  with  the  temperature. 

The  formula  of  Dale  and  Gladstone  is  far  more  accurate 

2  ' 

than  the  expression — ,  which  was  proposed   earlier, 

d 

and  it  is  preferable  to  that  of  Lorenz-Lorentz,4  which 
is:  — 


Recently,  Edwards  6  has  tested  the  formula  — 

n  —  i 

~^d~' 

and  has  shown  that  it  holds  for  a  number  of  substances, 
over  a  considerable  range  of  temperature. 

None  of  these  expressions,  however,  are  perfectly  gen- 
eral, and  without  the  introduction  of  specific  constants, 
they  do  not  show  an  exact  relation  between  refractivity 

1  Phil.  Trans.  (1858),  887.     Ibid,,  1863.         3  ibid.,  132,  202;  133,  i. 

2  Pogg.  Ann.,  123,  595.  4  Wied.  Ann.,  u,  70;  9,  641. 

6  Amer.  Chem.  Journ.,  16,  625;   17,  473. 
C 


1 8  ELECTROLYTIC   DISSOCIATION 

and  density.  Indeed,  it  is  not  at  all  certain  that  such  a 
relation  exists. 

Relations  between  refractivity,  and  composition  and  con- 
stitution, have,  however,  been  worked  out,  and  a  few  of 
these  will  now  be  considered. 

Dale  and  Gladstone *  found  that  isomeres  of  similar  con- 
stitution have  very  nearly  the  same  specific  refractivity. 
In  homologous  series  this  quantity  increases  regularly. 
They  drew  the  general  conclusion,  that  "  every  liquid  has  a 
specific  refractivity,  composed  of  the  specific  refractivities 
of  the  elements  in  the  compound,  modified  by  the  kind  of 
union." 

Landolt2  compared  the  "refraction  equivalents"  of  sub- 
stances, calculating  them  from  the  formula  — 

m(n  —  i ) 

~T~ 

in  which  m  is  the  molecular  weight  of  the  substance,  and 
the  other  symbols  have  the  same  significance  as  in  the 
Dale-Gladstone  expression. 

The  relation  between  composition  and  refraction  equiva- 
lents was  worked  out,  and  it  was  found  that  equal  differ- 
ences in  composition  correspond  to  equal  differences  in 
refraction  equivalents. 

Landolt  showed,  also,  that  the  refraction  equivalent  of  a 
compound  is  approximately  the  sum  of  the  refraction 
equivalents  of  its  parts. 

He  investigated,  further,  the  relation  between  constitu- 
tion and  refraction  equivalents,  by  studying  metameric 
substances.  A  few  results  are  given :  — 

1  Phil.  Trans.,  1863.  2  Pogg.  Ann.,  117,  353  ;   122,  545;   123,  595. 


THE   EARLIER   PHYSICAL  CHEMISTRY  19 

SUBSTANCE  REFRACTION  EQUIVALENT 

Propionic  acid,  C3H6O2  28.57 

Methyl  acetate,  C3H6O2  29.36 

Ethyl  formate,  C3H6O2  29.18 

Valeric  acid,  C5H10O2  44-O5 

Methyl  butyrate,  C5H10O2  43.97 

Butyl  alcohol,  C4H10O  36.11 

Ethyl  ether,  C4H10O  36.26 

Isomeric  substances  are  thus  seen  to  have  the  same 
refraction  equivalents. 

J.  W.  Briihl  has  carried  out  elaborate  investigations,  since 
the  year  iSSo,1  on  the  refractive  power  of  liquids.  His 
work,  which  has  now  extended  over  nearly  twenty  years, 
has  brought  to  light  many  interesting  and  important  rela- 
tions. He  took  up  the  effect  of  carbon,  in  its  different 
forms  of  combination,  upon  refractive  power,  and  showed 
that  doubly  united  carbon  exerted  a  different  influence 
from  carbon  united  by  single  bonds.  Each  double  union 
in  a  compound  increases  the  refraction  equivalent  about 
two  units.  He  thus  showed  the  influence  of  constitution 
on  refractivity.  He  also  found  that  oxygen,  in  its  different 
forms  of  combination,  had  different  effects  on  refractivity. 

The  question  of  the  effect  of  symmetry  on  refractive 
power  has  also  been  studied.  Two  isomeric  compounds, 
the  one  symmetrical,  the  other  asymmetrical,  have  been 
studied  with  the  following  results  :  — 

SUBSTANCE  REFRACTION  EQUIVALENT 

j  Ethylene  chloride  20195 

[  Ethylidene  chloride  21.08 

I  Ethylene  bromide  26.84 

{  Ethylidene  bromide  27.31 
1  Liebig's  Ann.,  200,  139. 


20  ELECTROLYTIC  DISSOCIATION 

The  unsym metrical  compound  has  a  larger  refraction 
equivalent  than  the  symmetrical. 

The  refraction  values  of  a  number  of  elements  have 
been  worked  out,  and  also  the  differences  in  the  refraction 
values  of  certain  elements  in  different  forms  of  combina- 
tion. Refractivity,  therefore,  can  be  and  has  been  used  to 
throw  light  on  the  question  of  constitution.  Bruhl  has 
applied  the  method  of  refractivity  to  the  problem  of  the 
constitution  of  benzene.  How  are  the  carbon  atoms 
united  in  benzene  ?  If  by  a  single  bond,  they  will  have 
a  different  refractive  power  than  if  they  were  doubly 
united.  From  the  power  of  benzene  to  refract,  Bruhl  was 
led  to  the  conclusion  that  there  are  three  single  and  three 
double  bonds  in  the  molecule,  which  is  expressed  thus :  — 


This  is  the  well-known  benzene  formula  of  Kekule". 

It  should  be  stated,  that  it  is  not  safe  to  place  unlimited 
confidence  in  a  method  like  the  above  for  determining  the 
constitution  of  chemical  compounds.  The  same  problem 
has  been  attacked  by  Julius  Thomsen,  with  very  differ- 
ent result,  using  a  thermochemical  method.  Thomsen's 
method  is  based  upon  the  principle,  that  when  a  compound 
is  burned  a  different  amount  of  heat  is  liberated  if  the 
carbon  atoms  are  united  by  single  or  double  bonds,  than 
if  they  are  united  by  triple  bonds.  He  determined  the 
heat  of  combustion  of  benzene,  and  found  that  it  cor- 


THE   EARLIER   PHYSICAL  CHEMISTRY  21 

responds  to  nine  single  bonds  between  the  carbon  atoms,1 
which  would  be  expressed  thus  :  — 


HC 


HC 
^, 

CH 


This  is  the  well-known  prism  formula  of  benzene,  sug- 
gested and  defended  by  Ladenburg.  This  apparent  di- 
gression is  made,  to  show  the  caution  which  is  necessary  in 
accepting  conclusions  based  upon  work  such  as  that  above 
described. 

Rotation  of  the  Plane  of  Polarization.  —  When  a  beam  of 
polarized  light  is  passed  through  certain  liquids,  the  plane 
of  polarization  is  changed.  Sometimes  it  is  turned  in  the 
one  direction,  sometimes  in  the  other.  This  property  is 
not  confined  to  liquids,  but  is  possessed  also  by  solids  and 
gases.  Substances  which  have  this  property  are  said  to 
be  optically  active.  According  as  the  substance  rotates 
the  plane  of  polarization  in  the  one  or  in  the  other  direc- 
tion, it  is  termed  dextro-  or  laevo-rotatory. 

The  direction  and  amount  of  rotation  depend  chiefly 
upon  the  nature  of  the  substance.  The  rotation  depends, 
also,  upon  the  thickness  of  the  layer,  the  wave-length  of 
light,  and  the  temperature.  Comparable  results  can, 
therefore,  be  obtained  only  by  keeping  all  of  the  con- 
ditions constant,  and  then  studying  the  kind  and  amount 
of  rotation  which  different  compounds  produce. 

l  Ber.  d.  chem.  Gesell.,  13,  1808. 


22  ELECTROLYTIC   DISSOCIATION 

The  specific  rotatory  power  of  a  liquid  has  been  defined 
by  Biot,  as  the  rotation  produced  by  a  layer  one  decimetre 
in  length.  But  since  different  liquids  have  different  den- 
sities, this  would  contain  different  amounts  of  substance. 
The  specific  rotatory  power  r  is  obtained  by  dividing  the 
angle  a,  through  which  a  column  of  liquid  of  length  /,  and 
density  d,  rotates  the  plane  of  polarization,  by  Id. 

r=2- 
Id 

In  order  to  compare  the  rotatory  power  of  liquids  we  must 
deal  with  comparable  quantities,  and  most  conveniently 
with  molecular  quantities.  If  m  is  the  molecular  weight 
of  the  substance,  this  must  be  multiplied  into  the  above 
expression.  The  molecular  rotatory  power  mr  would 

then  be  :  — 

ma 


This  unit  is  usually  divided  by  one  hundred. 

Some  exceedingly  interesting  relations  between  rotatory 
power,  and  composition  and  constitution,  have  been  worked 
out.  There  is  quite  a  large  number  of  substances  which 
exist  in  different  forms,  one  rotating  the  plane  of  polariza- 
tion to  the  right,  the  other  to  the  left.  Pasteur1  pointed 
this  out  in  connection  with  the  tartaric  acids.  There  is 
a  dextro-rotatory  tartaric  acid,  and  a  laevo-rotatory  tartaric 
acid,  and  inactive  racemic  acid.  The  latter  is  produced  by 
mixing  solutions  of  the  dextro-  and  Isevo-varieties,  and,  on 
the  other  hand,  racemic  acid  can  be  separated  into  dextro- 
and  laevo-tartaric  acids.  This  separation  is  accomplished 

1  Ann.  Chim.  Phys.,  28,  56  (1850). 


THE  EARLIER   PHYSICAL  CHEMISTRY  23 

by  preparing  the  sodium-ammonium  salt  of  racemic  acid, 
and  allowing  it  to  crystallize.  Salts  of  dextro-  and  laevo- 
tartaric  acids  will  separate,  and  can  be  distinguished  by 
the  difference  in  crystal  forms.  Certain  right-handed 
hemihedral  planes  appear  on  the  salt  of  the  dextro-acid, 
and  left-handed  planes  on  the  salt  of  the  laevo-acid.  There 
is  also  a  fourth  tartaric  acid,  which  is  inactive,  but  this 
can  be  transformed  into  the  other  modifications. 

There  are  several  other  examples  known  of  a  substance 
existing  in  a  dextro-  and  laevo-modification,  and  also  in  an 
inactive  form ;  and  by  combining  the  active  modifications, 
the.  inactive  is  formed,  and  from  the  inactive  form  the 
active  may  be  obtained. 

A  direct  study  of  the  relation  between  optical  activity, 
and  composition  and  constitution,  will  be  considered  more 
in  detail.  We  will  deal  with  the  compounds  of  carbon.  It 
was  observed  by  the  French  chemist,  Le  Bel,1  and  a  little 
later  by  van't  Hoff,2  that  every  carbon  compound  which 
is  optically  active  can  be  represented  as  containing  a  car- 
bon atom  in  combination  with  four  different  atoms  or 
groups.  Take  the  simplest  case,  that  of  lactic  acid.  We 
have  :  — 

CH3 

H  — C— COOH 

I 
OH 

Le  Bel  ascribed  optical  activity  to  the  asymmetrical  nature 
of  such  an  arrangement,  but  van't  Hoff  went  much  far- 

1  Bull.  Soc.  Chim.  [2],  22,  337  (1874). 

2  Ibid.,  23,  295  (1875). 


24  ELECTROLYTIC  DISSOCIATION 

ther,  and  tried  to  show  how  the  atoms  are  actually  ar- 
ranged in  space.  He  represented  the  central  carbon  atom 
of  the  system,  as  placed  at  the  centre  of  a  regular  tetrahe- 
dron, with  its  four  bonds  acting  in  the  directions  of  the 
solid  angles.  At  those  angles  are  placed  the  four  atoms, 
or  groups,  in  combination  with  the  central  carbon  atom. 
If  these  atoms,  or  groups,  are  the  same,  we  would  have  a 
perfectly  symmetrical  arrangement,  and  every  atom  would 
bear  the  same  relation  to  the  molecule  as  every  other 
atom.  Take  the  case  of  marsh  gas,  the  four  hydrogen 
atoms  should  each  bear  the  same  relation  to  the  molecule, 
and  such  has  been  shown  to  be  the  case  by  the  elaborate 
work  of  Henry.  If  either  two  of  the  atoms,  or  groups,  at 
the  corners  of  the  tetrahedron  are  the  same,  then  it  is  im- 
possible to  so  arrange  them  that  two  tetrahedra,  contain- 
ing the  same  four  groups  at  the  corners,  could  not  be 
completely  superimposed.  But  if  all  four  atoms,  or  groups, 
are  different,  then  two  tetrahedra  containing  these  at  the 
corners  can  never  be  superimposed,  but  bear  the  relation 
to  one  another  of  an  object  and  its  image  in  a  mirror. 

If  this  asymmetrical  arrangement  is  the  cause  of  optical 
activity,  then  only  those  carbon  compounds  could  be  opti- 
cally active  which  have  four  different  atoms,  or  groups, 
combined  with  the  central  carbon  atom.  Of  all  the  cases 
of  optical  activity  known  among  carbon  compounds,  there 
is  only  one  possible  exception.  Baeyer l  has  described  a 
dipentene,  which  he  thinks  does  not  contain  an  asymmetric 
carbon  atom,  and  which  is,  however,  optically  active.  But 
this  cannot  be  cited  as  a  positive  exception,  since  the  con- 
stitution of  this  substance  is  not  definitely  established. 

1  Ber.  d.  chem.  Gesell.,  27,  454. 


THE   EARLIER   PHYSICAL  CHEMISTRY  25 

Another  consequence  of  the  van't  Hoff  theory  is,  that 
whenever  a  dextro-rotatory  substance  appears,  a  laevo 
must  also  be  formed,  and  such  is  the  fact.  Of  the  large 
number  of  cases  known,  there  is  no  exception  to  this 
rule. 

If  optical  activity  is  due  to  the  presence  of  an  asymmet- 
ric carbon  atom,  then,  whenever  we  have  such  a  carbon 
atom  present,  we  ought  to  have  optical  activity.  There 
are,  however,  many  compounds  known,  which  contain  an 
asymmetric  carbon  atom,  yet  do  not  show  optical  activity. 
This  is  explained  by  assuming  that  there  are  present  an 
equal  number  of  dextro-  and  laevo-molecules,  and  optical 
inactivity  is  the  result.  Similarly,  if  there  are  two  asym- 
metric carbon  atoms  in  the  same  molecule,  these  may 
exactly  neutralize  each  other's  influence  on  polarized  light, 
as  in  the  case  of  the  fourth  variety  of  tartaric  acid. 

It  is  difficult  to  overestimate  the  importance  of  these 
suggestions  by  Le  Bel  and  van't  Hoff.  They  underlie 
all  that  has  been  done  along  the  line  of  stereochemistry, 
and  this  is  certainly  one  of  the  most  important  advances 
which  has  been  made  in  organic  chemistry  in  the  last 
quarter  of  a  century. 

This  suggestion  of  the  tetrahedron  as  the  spatial  ar- 
rangement in  carbon  compounds  has  been  developed  much 
farther  by  Wislicenus l  than  was  done  by  van't  Hoff.  The 
former  has  shown  how  this  arrangement  is  capable  of 
accounting  satisfactorily  for  the  transformations  of  male'fc 
and  fumaric  acids;  of  the  malic  acids;  and,  what  is  even 
more  interesting,  it  furnishes  a  beautiful  explanation  of 

1  Monograph,  Ueber  die  raumliche  Anordnung  der  Atome  in  organischen 
Molekiilen,  Leipzig. 


26  ELECTROLYTIC   DISSOCIATION 

the  optical  behavior  of  the  four  tartaric  acids ;  facts 
which  hitherto  had  been  empirically  established,  but  whose 
significance  was  entirely  unknown.  While  space  will  not 
permit  us  to  enter  into  a  discussion  of  this  monograph  by 
Wislicenus,  yet  we  should  again  call  attention  to  its  unus- 
ual interest  and  importance  for  all  who  are  interested  in 
the  philosophy  of  organic  chemistry. 

The  suggestion  by  van't  Hoff  to  account  for  optical 
activity  has  been  further  extended  by  Guye.1  If  optical 
activity  is  due  to  the  groups  being  different  at  the  four 
corners  of  the  tetrahedron,  —  to  an  asymmetrical  arrange- 
ment, —  then  by  changing  the  degree  of  asymmetry,  the 
degree  of  optical  activity  ought  also  to  be  changed.  If  we 
have  a  carbon  atom  surrounded  by  four  different  atoms  or 
groups,  the  centre  of  gravity  of  the  system  will  lie  off  of 
the  planes  of  symmetry.  If  now  we  replace  one  of  the 
atoms  or  groups  by  one  having  a  greater  weight,  the  centre 
of  gravity  of  the  system  will  be  moved  toward  the  heavier 
substituent.  By  changing  the  masses  of  the  atoms  or 
groups,  the  centre  of  gravity  of  the  system  can  be  changed, 
first  in  one  and  then  in  another  direction. 

Guye  has  shown,  in  a  large  number  of  cases,  that  as  the 
centre  of  gravity  of  the  system  is  changed,  by  intro- 
ducing lighter  or  heavier  groups,  the  optical  activity  of 
the  substance  changes,  and  in  the  way  that  would  be  ex- 
pected. As  the  asymmetry  was  increased,  optical  activity 
in  general  increased. 

By  introducing  groups  of  the  weights  desired,  the  centre 
of  gravity  could  often  be  changed  from  one  side  of  the 
molecule  to  the  other,  and  in  a  number  of  such  cases  the 

1  Compt.  rend.,  no,  714. 


THE   EARLIER   PHYSICAL  CHEMISTRY  27 

nature  of  the  rotation  was  changed  —  a  dextro-rotatory 
substance  becoming  laevo-rotatory,  and  the  reverse. 

There  are  some  cases  known  which  cannot  be  entirely 
reconciled  with  the  views  of  Guye.  Work  of  this  kind 
is  undoubtedly  of  the  very  highest  importance,  since  it 
throws  light  on  the  inner  arrangement  of  the  atoms  and 
groups  in  the  molecule. 

Another  outcome  of  the  stereochemical  conception  of 
van't  Hoff,  with  respect  to  carbon,  is  the  recent  work 
which  has  been  done  on  the  stereochemistry  of  nitrogen. 
Hantzsch  and  Werner1  have  shown,  that  if  we  represent 
the  nitrogen  atom  as  being  placed  at  one  of  the  angles  of 
a  tetrahedron,  we  can  explain  the  differences  in  constitu- 
tion which  undoubtedly  exist  between  many  of  the  isomeric 
substances  containing  nitrogen ;  differences  for  which  it  is 
impossible  to  account,  in  many  cases,  by  the  ordinary 
methods  of  representing  constitution,  which  do  not  take 
into  account  spatial  relations. 

Although  the  work  of  Wislicenus,  Guye,  and  Hantzsch 
and  Werner  was  done  in  the  last  few  years,  yet  it  is  the 
direct  outcome  of  the  suggestion  made  by  van't  Hoff  in 
l&7$>  which  is  more  than  ten  years  before  the  newer  de- 
velopments  in  physical  chemistry  began.  It,  therefore, 
seems  not  to  be  entirely  out  of  place  to  refer  to  this  recent 
work  under  the  head  of  the  earlier  physical  chemistry,  of 
which  it  is  the  direct  consequence. 

Magnetic  Rotation  of  the  Plane  of  Polarization.  —  It  was 
discovered  by  Faraday,2  that  substances  in  general  have 
the  power  to  rotate  the  plane  of  polarization  of  light,  when 
placed  in  a  suitable  position  in  a  magnetic  field.  An  electro- 

1  Ber.  d.  chem.  Gesell.,  23,  u,  1243,  2764,  2769.         2  Pogg.  Ann.,  68,  105. 


28  ELECTROLYTIC   DISSOCIATION 

magnetic  field  is  the  most  convenient,  the  current  flowing 
in  a  plane  at  right  angles  to  the  direction  in  which  the  ray 
of  light  moves.  The  amount  of  rotation  depends  on  the 
strength  of  the  magnetic  field,  length  of  layer  of  substance, 
the  temperature,  and  the  nature  of  the  substance.  To  dis- 
cover any  relations  between  magnetic  rotation  and  compo- 
sition, every  one  of  the  above  conditions  must  be  kept 
constant,  from  one  substance  to  another. 

The  work  of  Becquerel1  brought  out  some  relations, 
such  as  that  the  rotatory  power  of  the  alcohols  increased 
with  increase  in  molecular  weight;  but  by  far  the  most 
elaborate  investigation  of  this  phenomenon  we  owe  to 
W.  H.  Perkin.2  He  chose  as  his  unit  the  molecular  rota- 
tion of  water,  and  compared  other  substances  with  it.  A 
few  examples  are  given  :  — 

SUBSTANCE  MOLECULAR  ROTATION 

Methyl  alcohol,  CH4O  1.64 


Ethyl  alcohol,     C2H6O  2.780^ 

Propyl  alcohol,  C3H8O  3.76 

Formic  acid,       H2CO2 


-. 

^0.908 
Acetic  acid,        C2H4O2  2-525\ 

y>0-937 

Propionic  acid,  C3H6O2  3-462' 

^I.OIO 

Butyric  acid,       C4H8O2  4.4 7  Y 

These  results,  taken  from  a  large  number,  show,  for  a 
homologous  series,  a  constant  difference  in  the  magnetic 

1  Ann.  Chim.  Phys.  [4],  22,  5.          2  Journ.  prakt.  Chem.  [2],  31,  481 ;  32,  523. 


THE   EARLIER   PHYSICAL  CHEMISTRY  29 

rotation  produced  by  the  constant  difference  in  composi- 
tion of  CH2.  The  effect  of  constitution  on  magnetic  rota- 
tion can  be  seen  by  comparing  isomeric  compounds. 

SUBSTANCE  MAGNETIC  ROTATION 

JPropyl  alcohol,  C3H8O  3.768 

\  Isopropyl  alcohol,      C3H8O  4.019 

fEthylene  chloride,     C2H4C12  5.485 

JEthylidene  chloride,  C2H4C12  5.335 

These  examples  suffice  to  bring  out  the  fact,  that 
isomeric  substances  have  different  magnetic  rotation, 
showing  the  effect  of  constitution  on  this  property. 

Perkin  has  continued  his  work  on  magnetic  rotation  up 
to  the  present,  and  some  of  his  more  important  com- 
munications are  referred  to  below.1 

J.  W.  Rodger  and  W.  Watson2  have  published  an  inves- 
tigation on  magnetic  rotation,  where  a  stronger  magnetic 
field  was  used,  and,  consequently,  the  amount  of  rotation  to 
be  measured  was  greater.  Their  paper  is  devoted  mainly 
to  a  description  of  their  apparatus,  and  contains  too  few 
results  to  warrant  any  generalization.  It  is  to  be  hoped 
that  this  work  will  be  continued,  using  the  stronger  mag- 
netic field. 

Conclusion  from  the  Preceding  Work.  —  On  examining 
the  work  thus  far  described,  we  are  impressed  by  the  large 
number  of  relations  which  have  been  pointed  out  between 
physical  properties,  and  composition  and  constitution. 
But  we  are  also  impressed  by  the  fact  that  these  relations 

i  Chem.  News,  60, 253 ;  62, 255 ;  64, 19 ;  65, 284 ;  66, 277 ;  67, 143 ;  68, 302 ;  69,  224 ; 
71,  123;  73,  301.  Journ.  Chem.  Soc.,  59,  981 ;  61,  287  ;  61,  800;  65,  815  ;  69,  1025. 
Ztschr.  phys.  Chem.,  21,  451 ;  21,  671.  2  Ztschr.  phys.  Chem.,  19,  323. 


3O  ELECTROLYTIC  DISSOCIATION 

are  only  approximations ;  they  are  not  sharply  defined 
and  rigorous.  A  relation  was  often  discovered,  which,  at 
first,  seemed  to  be  fairly  exact,  but  as  the  experimental 
work  became  more  refined,  a  larger  number  of  exceptions 
appeared.  Thus,  in  many  cases,  what  seemed  to  be  a 
quantitative  relation  was  merely  a  qualitative  one. 

We  feel,  throughout  this  entire  work,  the  purely  empir- 
ical nature  of  the  generalizations  reached,  and  that  they 
are  very  incomplete  expressions  of  the  truth.  There  is  a 
lack  of  any  definite,  mathematical  conception,  in  terms  of 
which  this  earlier  work  can  be  interpreted. 

The  Study  of  Solutions. — The  physical  properties  of 
substances  may  be  studied  when  they  are  isolated,  or  when 
they  are  mixed  with  other  substances.  Under  the  latter 
condition,  one  substance  is  said  to  be  dissolved  in  the  other, 
and  we  have  to  do  with  solutions.  A  number  of  the  prop- 
erties of  solutions  were  early  investigated.  Graham 1 
studied  the  phenomenon  of  diffusion,  and  Fick2  pointed 
out  that  diffusion  depends  upon,  and  is  proportional  to,  the 
difference  in  concentration  of  the  solutions.  Blagden3 
discovered,  more  than  a  hundred  years  ago,  that  the  lower- 
ing of  the  freezing-point  of  water  by  a  dissolved  substance 
is  proportional  to  the  amount  of  substance  present.  The 
same  fact  was  rediscovered  by  Riidorff,4  and,  later,  Coppet5 
showed  that  the  molecular  lowering  of  the  freezing-point, 
produced  by  closely  allied  substances,  is  very  nearly  con- 
stant. 

Raoult6  studied  the  freezing-point  lowering  of  solutions 

1  Liebig's  Ann.,  77,  56,  129 ;  80,  197.      8  Phil.  Trans.,  78,  277. 

2  Pogg.  Ann.,  94,  59.  *  Pogg.  Ann.,  114,  63  ;   116,  55 ;    145,  599. 
6  Ann.  Chim.  Phys.  [4],  23,  366;    25,  502;  26,  98. 

6  Compt.  rend.,  94,  1517;   95,  188,  1030;     Ann.  Chim.  Phys.  [6],  2,  66. 


THE   EARLIER   PHYSICAL   CHEMISTRY  31 

in  solvents  other  than  water,  and  arrived  at  the  generali- 
zation, that  a  molecule  of  any  substance,  in  one  hundred 
molecules  of  a  solvent,  lowers  the  freezing-point  of  the 
.solvent  by  a  nearly  constant  amount.  These  investigations 
by  Raoult  on  freezing-point  lowering  were  very  elaborate, 
including  a  large  number  of  solutions  in  acetic  acid,  formic 
acid,  benzene,  nitrobenzene,  ethylene  bromide,  etc. 

The  lowering  of  the  vapor-pressure  of  a  solvent  by  a 
dissolved  substance  was  early  investigated.  Wullner1 
pointed  out  that  the  lowering  of  the  vapor-pressure  of 
water  by  dissolved  substances  is  proportional  to  the 
amount  of  substance,  and  Raoult 2  studied  the  influence  of 
temperature,  concentration,  and  nature  of  dissolved  sub- 
stance, on  the  depression  of  the  vapor-tension  of  the 
solvent.  Raoult3  worked  with  a  number  of  solvents,  and 
found  that  the  depression  of  the  vapor-tension  produced 
by  one  molecule  of  substance  in  one  hundred  molecules  of 
solvent  was  the  same  for  different  solvents.  Raoult  also 
showed  how  the  lowering  of  the  freezing-point  of  a  solvent 
by  a  dissolved  substance,  and  also  the  lowering  of  its  vapor- 
tension,  may  be  used  to  calculate  the  molecular  weight  of 
the  substance  in  solution. 

Other  Lines  of  Work.  —  The  earlier  physical  chemists 
were  not  all  engaged  with  problems  such  as  we  have  been 
considering.  They  measured  the  heat  liberated  in  chem- 
ical reactions.  They  studied  the  behavior  of  substances 
when  submitted  to  the  action  of  the  electric  current.  The 
velocity  with  which  chemical  reactions  take  place,  and  the 
conditions  of  equilibrium,  were  investigated.  And  the  dif- 

l  Pogg.  Ann.,  103,  529;  105,  85 ;  no,  564.  2  Compt.  rend.,  103,  1125. 

*  Ibid.,  104,  1430;  Ann.  Chim.  Phys.  [6] ,  15,  375  ;  Ztschr.  phys.  Chem.,  2,  353. 


32  ELECTROLYTIC   DISSOCIATION 

ferent  powers  of  substances  to  react,  as  depending  upon 
their  composition  and  constitution,  were  carefully  deter- 
mined. 

This  brief  account  of  the  nature  and  condition  of  phys- 
ical chemistry,  before  the  theory  of  electrolytic  dissociation 
arose,  would  be  unsatisfactory,  and,  perhaps,  misleading, 
without  some  statement  as  to  the  development  of  thermo- 
chemistry, electrochemistry,  and  chemical  affinity.  By 
knowing  the  condition  of  the  several  branches  of  physical 
chemistry,  before  the  new  conceptions  arose,  we  can  see 
the  more  clearly  what  changes  have  been  introduced, 
what  advances  made  by  them. 

THE  DEVELOPMENT  OF  THERMOCHEMISTRY 

The  quantitative  study  of  the  amount  of  heat  liberated 
in  chemical  reactions  was  begun  very  early,  and  has  been 
continued  from  the  time  of  Robert  Boyle  to  the  present. 
The  problem,  in  one  form  or  another,  has  attracted  the 
attention  of  men  like  Davy,  Lavoisier,  and  Laplace.  In- 
deed, the  very  important  discovery  was  made  by  the  last 
two,1  that  just  as  much  heat  is  required  to  decompose  a 
compound  into  its  constituents  as  was  liberated  when  the 
constituents  united  to  form  the  compound.  But  the  begin- 
ning of  modern  thermochemistry  dates  from  the  time  of 
G.  H.  Hess.2 

Work  of  Hess.  —  Hess  discovered  the  principle  which  has 
come  to  be  known  as  the  "  Constancy  of  the  sum  of  the 
heats  of  reaction."  If  a  chemical  transformation  takes 
place  in  one  stage,  a  certain  amount  of  heat  is  liberated, 
which  we  will  call  a.  If  the  transformation  takes  place  in 

1  CEuv.  de  Lav.,  II,  287.  2  Pogg.  Ann.,  50,  385  (1840). 


THE  EARLIER   PHYSICAL   CHEMISTRY  33 

two  stages,  in  which,  respectively,  h  and  c  amounts  of  heat 
are  liberated,  we  always  have,  h  +  c  =  a.  This  is  perfectly 
general,  regardless  of  the  number  of  stages  involved  in  the 
transformation.  The  discovery  of  this  principle  makes 
it  possible  to  study,  thermochemically,  a  great  number  of 
reactions  which  are  comparatively  complex  taking  place 
in  more  than  one  stage. 

In  addition  to  this  important  discovery,  Hess  made 
another  of  very  wide  significance.  He  observed  that  when 
solutions  of  neutral  salts  are  mixed,  there  is  little  or  no 
heat  liberated  or  absorbed.  He  concluded,  that  the  heat 
consumed  in  decomposing  the  salts  was  exactly  equal  to 
that  liberated  in  the  formation  of  the  new  salts  with  acid 
and  base  interchanged,  since  it  was  known  that  under 
the  conditions  that  solutions  of  two  salts  are  mixed,  four 
salts  are  always  formed,  provided  all  four  are  easily  solu- 
ble and  no  precipitate  is  produced.  This  has  come  to  be 
known  as  Hess's  law  of  the  therm oneutrality  of  salts. 
The  significance  of  this  law  was  not  understood  until  it 
was  fully  explained  by  the  theory  of  electrolytic  disso- 
ciation. 

Favre  and  Silbermann.  —  We  now  come  to  the  beautiful 
thermochemical  investigations  of  Favre  and  Silbermann.1 
They  greatly  improved  the  apparatus  and  method  used 
in  thermochemical  measurements.  The  calorimeter  which 
they  devised  is  the  same  in  principle  as  every  form  used 
since  their  time.  They  carried  out  elaborate  thermo- 
chemical investigations,  which  were  undoubtedly  the  most 
accurate  up  to  their  time. 

Thermochemical  investigations  since  the  time  of  Favre 

l  Ann.  Chim.  Phys.  [3]  ,'34,  357 ;  36,  I ;  37,  406.   t 


34  ELECTROLYTIC  DISSOCIATION 

and  Silbermann  have  centred  around  two  men:  Berthelot 
in  Paris,  and  Julius  Thomsen  in  Copenhagen.  Much 
work  has  also  been  done  by  pupils  of  these  men,  either 
working  with  them  or  independently. 

Work  of  Berthelot.  —  Berthelot1  began  his  very  elaborate 
thermochemical  investigations  in  1865,  and  these  have  ex- 
tended over  a  long  period.  The  results  of  his  work  are 
published  in  his  well-known  book,  of  two  volumes,  "  Essai 
de  Mecanique  Chimique."  The  three  principles  which  he 
developed  in  his  work  are :  — 

First,  the  heat  liberated  in  a  chemical  reaction  depends 
only  on  the  condition  of  the  system  at  the  beginning  and 
at  the  end,  and  not  at  all  on  the  intermediate  stages. 

Second,  the  heat  evolved  in  a  chemical  process  is  a 
measure  of  the  corresponding  chemical  and  physical  work. 

Third,  every  chemical  reaction  tends  to  form  those  sub- 
stances which  are  formed  with  the  greatest  evolution  of  heat. 

This  last  principle  has  come  to  be  known  as  the  law  of 
maximum  work,  but  would  better  be  known  as  the  law  of 
maximum  heat  evolution. 

The  last  of  the  three  principles  announced  by  Berthelot 
has  attracted  by  far  the  most  attention.  As  an  expression 
of  a  perfectly  general  truth,  it  is,  of  course,  not  exact. 
There  are  many  exceptions  known  to  it,  and  some  of  these 
were  recognized  and  pointed  out  by  Berthelot  himself. 
And  yet,  notwithstanding  the  exceptions,  if  one  will  care- 
fully "read  the  "  Essai  de  Mecanique  Chimique,"  the  im- 
pression is  almost  sure  to  be  left  that  here  is,  at  least, 
the  kernel  of  a  great  truth,  even  if  it  is  expressed  in  an 
imperfect  and  not  sufficiently  comprehensive  manner. 

1  Ann.  Chim.  Phys.  [4],  6,  290;  28,  94. 


THE  EARLIER  PHYSICAL  CHEMISTRY  35 

Much  of  the  criticism  of  this  third  principle,  whether  its 
true  discoverer  be  Berthelot1  or  Julius  Thomsen,2  is  evi- 
dently not  entirely  well  founded,  if  all  that  Berthelot  has 
written  concerning  it  is  taken  into  account. 

Work  of  Julius  Thomsen.  —  The  thermochemical  work 
of  Julius  Thomsen  has  been  collected  into  four  volumes, 
and  published  under  the  title  of  "  Thermochemische  Un- 
tersuchungen."  This,  taken  as  a  whole,  undoubtedly  con- 
tains the  most  elaborate  and  accurate  thermochemical 
measurements  which  have  ever  been  made. 

In  order  that  a  reaction  may  be  studied  thermochem- 
ically,  one  condition  is  that  it  should  proceed  rapidly  to 
the  end.  Many  reactions  between  organic  compounds  do 
not  fulfil  this  condition.  Indeed,  most  organic  reactions 
are  relatively  slow.  To  study  such  reactions  thermo- 
chemically,  some  means  must  be  devised  which  would 
accelerate  the  velocity  of  the  reaction.  Berthelot3  im- 
proved the  form  of  apparatus  which  had  already  been 
suggested  for  this  purpose.  A  thick-walled,  steel  cylinder, 
lined  on  the  inside  with  platinum  or  enamel,  is  used  for 
accelerating  the  velocity  of  such  reactions  as  organic  com- 
bustions. The  substance  to  be  burned  is  placed  on  a 
suitable  arrangement,  and  introduced  into  the  "bomb." 
This  is  then  tightly  closed,  and  filled  with  oxygen  under 
high  pressure.  The  substance  is  ignited  by  an  electric 
current;  the  combustion  proceeds  very  rapidly,  and  the 
heat  set  free  is  measured  in  some  convenient  form  of 
calorimeter.  The  use  of  the  Berthelot  bomb  has  greatly 
widened  the  field  of  thermochenifcal  investigation. 

1  Ann.  Chim.  Phys.  [5],  4,  6;   [4],  18,  103.         *"BSFrtr.  chem.  Gesell.,  6,  423. 
8  Ann.  Chim.  Phys.  [5],  23,  160. 


36  ELECTROLYTIC  DISSOCIATION 

Some  of  the  most  accurate  thermochemical  measure- 
ments, in  which  the  bomb  has  been  employed,  have  been 
made  by  Stohmann,1  in  Leipzig  (who  worked  for  a  time 
with  Berthelot),  and  by  his  assistant,  Langbein. 

Thermochemical  Results.  —  A  few  thermochemical  re- 
sults will  suffice  to  bring  out  the  kind  of  relations  which 
have  been  discovered  by  such  work. 

The  heat  evolved  when  acids  and  bases  neutralize  each 
other  has  been  carefully  investigated.  We  will  give  a  few 
results  for  the  strong  acids  and  strong  bases  :  — 


NaOH  +  HNO3  =  13680  cal. 
NaOH  +  HC1O3  =  13760  cal. 
NaOH  +  HBrO3  =  13780  cal. 
NaOH  +  HIO3  =  13810  cal. 
NaOH  +  HC1  =13700  cal. 
NaOH  +  HBr  =13700  cal. 
NaOH+  HI  =13  700  cal. 


In  the  above  table  the  base  is  kept  constant  and  the 
acid  changed ;  yet  the  heat  of  neutralization  of  equivalent 
quantities  is  nearly  a  constant.  A  few  results  will  be  cited 
in  which  a  given  acid  is  neutralized  with  a  number  of 

bases : — 

KOH  +  HC1=  1 3  700  cal. 

£Ba  (OH)2  +  HC1  =  13900  cal. 

£Sr  (OH),  +  HC1  =  13800  cal. 

£Ca  (OH)2  +  HC1  =  13900  cal. 

Here,  again,  the  heat  of  neutralization  is  nearly  a  con- 
stant, and  the  same  constant  as  in  the  preceding  case.  It 
can,  therefore,  be  stated,  that  the  heat  liberated,  when- 

i  Journ.  prakt.  Chem.,  33,  241;  35,40;  39,  509;  40,341;  42,  367;  43,  i ;  44, 
336;  45.332. 


THE  EARLIER   PHYSICAL  CHEMISTRY  37 

ever  a  strong  acid  is  neutralized  by  a  strong  base,  is  a  con- 
stant, within  experimental  error,  independent  of  the  nature 
of  the  acid  and  of  the  base.  If  either  the  acid  or  base  is 
weak,  a  different  heat  of  neutralization  is  found. 

The  meaning  of  these  facts  was  entirely  unknown  at 
the  time  of  their  discovery.  Why  should  the  heats  of 
neutralization  of  strong  acids  and  strong  bases  be  a  con- 
stant, and  why  should  the  heats  of  neutralization  of  weak 
acids  and  bases  be  different?  These  were  questions 
whose  meaning  was  not  even  suspected  before  the  theory 
of  electrolytic  dissociation  was  proposed.  These  facts,  as 
we  shall  see,  are  not  only  explicable  in  terms  of  that 
theory,  but  are  a  necessary  consequence  of  it.  Indeed, 
the  constancy  of  the  heat  of  neutralization  of  strong  acids 
and  strong  bases  is  a  very  good  argument  in  favor  of  the 
correctness  of  the  new  theory,  and  this  argument  is  even 
strengthened  by  the  fact  that  weak  acids  and  bases  have 
a  different  heat  of  neutralization. 

Certain  relations  between  the  composition  and  constitu- 
tion of  organic  compounds  and  their  heats  of  combustion 
have  been  worked  out.  Take  the  marsh-gas  series  of 
hydrocarbons. 

SUBSTANCE  HEAT  OF  COMBUSTION 

Methane,  CH4  211 900  cal.v 

\rs8soocal. 

Ethane,    C2H6  37O40ocal.^ 

\i588oocal. 

Propane,  C3H8  529200  cal.^ 

Ni58ooocal. 

Butane,     C4H10  687200  cal 

Pentane, 


38  ELECTROLYTIC  DISSOCIATION 

A  difference  of  CH2  produces  very  nearly  a  constant 
difference  in  the  heats  of  combustion  of  these  hydrocar- 
bons. The  constitution  of  these  compounds  seems  to  have 
no  effect. 

The  following  results  were  obtained  for  the  ethylene 
hydrocarbons  :  — 

SUBSTANCE  HEAT  OF  COMBUSTION 

Ethylene,      C2H4  3334°°  cal. 


5  9300  cal. 
Propylene,     C3H6 

i5790ocal. 
Isobutylene,  C4H8  650600  cal.<^ 

^157000  cal. 
Amylene,       C5H10  807600  cal. 

A  constant  difference  in  the  heats  of  combustion  is 
observed  here,  also,  for  the  constant  difference  in  compo- 
sition of  CH2;  and  this  is  the  same  difference  as  in  the 
case  of  saturated  hydrocarbons.  The  heats  of  combustion 
of  the  two  series  are  not  the  same,  because,  in  addition 
to  two  hydrogen  atoms  more  in  one  system  than  in  the 
other,  we  have  doubly  united  carbon  atoms.  And  when- 
ever there  is  double  or  triple  union  between  the  carbon 
atoms,  the  heat  of  combustion  is  affected  by  it. 

The  halogen  substitution  products  of  the  marsh-gas 
hydrocarbons  show,  also,  constant  differences  in  the  heats 

of  formation  :  — 

DIP.  DIP. 

CH3C1  22000  cal.  CH3Br  14200  cal.  7800  cal.  CH3I  2800  cal.  19200  cal. 
C2H5C1  29600  cal.  C2H5Br  21800  cal.  7800  cal.  C2H5I  9900  cal.  19700  cal. 
C3H7C1  36000  cal.  C3H7Br  29100  cal.  6900  cal. 

Relations  appear  for  the  alcohols  which  are  similar 
to  those  found  for  the  hydrocarbons.  The  difference 


THE  EARLIER   PHYSICAL  CHEMISTRY  39 

between  the  heats  of  combustion  of  members  of  a  homolo- 
gous series  of  alcohols  is  nearly  constant,  as  the  following 
results  will  show :  — 

SUBSTANCE  HEAT  OF  COMBUSTION 

Methyl  alcohol,  CH4O  182200  cal.v 

\i583oocal. 

Ethyl  alcohol,     C2H6O  340500  cal.^ 

\i58ioocal. 

Propyl  alcohol,  C3H8O  498600  ca\. 

The  effect  of  constitution  on  heat  of  combustion  is  seen 
in  the  fact,  that  primary  alcohols  have  larger  heats  of  com- 
bustion than  either  secondary  or  tertiary.  An  interesting 
application  of  the  effect  of  constitution  on  heat  of  com- 
bustion has  been  made  by  Julius  Thomsen,  in  the  case  of 
benzene,  to  which  reference  has  already  been  made. 

THE  DEVELOPMENT  OF  ELECTROCHEMISTRY 

The  decomposition  of  chemical  compounds  by  the  elec- 
tric current  has  attracted  the  attention  of  physicists  and 
chemists  ever  since  the  discovery  of  the  voltaic  element 
at  the  close  of  the  last  century.  The  comparatively  insig- 
nificant elements  which  were  first  constructed  sufficed, 
however,  to  effect  a  number  of  decompositions,  such  as  the 
electrolysis  of  metal  salts,  of  water  to  which  acid  has  been 
added,  etc.  But  it  remained  for  Sir  Humphry  Davy l  to 
construct  the  large  voltaic  'element  which  effected  such 
remarkable  decompositions,  and  led  to  the  discovery  of  the 
alkali  metals.  The  current  from  his  element  was  passed 
through  the  fused  oxides  of  potassium  and  sodium,  when 
small  globules  were  seen  to  rise  to  the  surface  of  the  mol- 

1  Qilb.  Ann.,  7,  114  (1801). 


4O  ELECTROLYTIC  DISSOCIATION 

ten  mass,  and  take  fire  on  contact  with  the  air.  Thus  were 
sodium  and  potassium  first  separated  from  their  compounds. 

Davy's  Electrochemical  Theory.  —  The  direct  decomposi- 
tion of  the  oxides  of  the  alkali  metals  by  the  electric  cur- 
rent, also  the  decomposition  of  acidulated  water,  and  a 
large  number  of  other  chemical  substances,  pointed  to 
some  close  relation  between  chemical  attraction  and  elec- 
trical attraction.  As  the  net  result  of  his  very  elaborate 
electrochemical  studies,  Davy  was  led  to  the  electrochem- 
ical theory  which  bears  his  name.  The  atoms  of  sub- 
stances, by  contact,  acquire  different  electrical  charges, 
and  these  atoms  then  attract  one  another,  because  they  are 
charged,  the  one  positive,  and  the  other  negative.  These 
charges  may  be  so  slight,  that  the  attraction  between  them 
will  not  be  sufficient  to  cause  the  atoms  to  change  their 
former  relations,  or  they  may  be  great  enough  to  effect 
such  a  rearrangement,  when  a  chemical  compound  will  be 
formed.  Chemical  attraction  between  atoms  is,  then,  but 
the  electrical  attraction  between  the  opposite  charges  which 
have  accumulated  upon  them,  due  to  their  contact  with 
one  another. 

Electrolysis  consists  in  destroying  the  difference  between 
the  charges  upon  the  atoms  in  the  compound,  the  nega- 
tively charged  atom  receiving  positive  electricity  from  the 
positive  pole,  to  which  it  is  attracted,  and  becoming  neutral ; 
the  positively  charged,  attracted  and  neutralized  at  the 
negative  pole.  The  compound  would  thus  necessarily  be 
broken  down  by  electrolysis,  since  the  force  which  held  its 
constituents  together  no  longer  exists. 

Berzelius'  Electrochemical  Theory.  —  The  theory  of  Ber- 
zelius  differed  fundamentally  from  that  of  Davy.  Accord- 


THE  EARLIER  PHYSICAL  CHEMISTRY  41 

ing  to  Davy,  an  atom,  as  such,  is  electrically  neutral,  and 
becomes  charged  positively  or  negatively  by  contact  with 
another  atom,  which  takes  a  charge  of  the  opposite  sign, 
Berzelius  claimed  that  every  atom  is  electrically  charged 
with  both  kinds  of  electricity.  These  exist  upon  the  atom, 
in  polar  arrangement,  and  the  electrical  character  of  the 
atom  depends  upon  which  is  present  in  excess.  One  is 
usually  present  in  large  excess,  giving  the  atom  a  decidedly 
positive  or  negative  character.  •  One  "  pole  "  is  usually 
much  stronger  than  the  other,  so  that  the  atom  reacts  as  if 
it  was  "  unipolar."  Chemical  attraction  is  but  the  electri- 
cal attraction  of  these  oppositely  charged  atoms,  and  the 
intensity  of  the  former  is  conditioned  by  the  magnitude  of 
the  latter. 

A  negatively  charged  atom  is  attracted  to  and  combines 
with  one  which  is  charged  positively.  The  magnitude  of 
these  opposite  charges  may  not  be  the  same,  and  the  com- 
pound formed  will  itself  be  electrically  positive  or  nega- 
tive, depending  upon  which  charge  upon  the  atoms  is  the 
greater.  Two  compounds,  the  one  charged  positively  and 
the  other  negatively,  may,  then,  in  turn,  combine,  forming 
a  still  more  complex  compound.  In  this  way  Berzelius 
attempted  to  account  for  the  more  complex  substances, 
such  as  the  so-called  double  compounds. 

The  theory,  as  put  forward  by  Berzelius,  did  not  long 
enjoy  freedom  from  adverse  criticism.  If  chemical  union  is 
produced  by  the  electrical  attraction  of  oppositely  charged 
atoms,  then,  as  soon  as  these  atoms  come  together,  the 
electrical  differences  would  disappear,  and  the  compound 
must  fall  apart.  As  soon,  however,  as  the  atoms  separated, 
they  would  become  oppositely  charged,  and  again  reunite. 


42  ELECTROLYTIC  DISSOCIATION 

There  would  thus  result  a  continued  decomposition  and 
reunion,  and  a  chemical  compound  would,  at  best,  be  in  a 
state  of  unstable  equilibrium.  This  would  apply  to  all 
chemical  compounds. 

But  the  theory  was  called  upon  to  meet,  apparently,  a 
more  serious  objection.  If  chemical  union  depends  only 
upon  the  attraction  of  the  opposite  electrical  charges  upon 
the  atoms,  then  the  properties  of  the  compound  formed 
must  depend  upon  the  nature  of  the  charges  upon  the 
atoms  in  the  compound.  It  was,  however,  found  to  be 
possible  to  substitute  the  three  hydrogen  atoms  in  acetic 
acid  by  three  chlorine  atoms,  passing  from  CH3COOH 
to  CClgCOOH.  And  the  remarkable  fact  was  discovered, 
that  the  properties  of  trichloracetic  acid  were  very  similar 
to  those  of  acetic  acid  itself. 

This,  Berzelius  himself  could  not  satisfactorily  reconcile 
with  his  theory.  Each  of  the  three  hydrogen  atoms  car- 
ried a  positive  charge,  while  the  three  chlorine  atoms  each 
carried  a  negative.  Yet  the  three  hydrogen  atoms,  with 
their  positive  charges,  could  be  replaced  by  the  three 
chlorine  atoms  with  their  negative  charges,  without  ma- 
terially changing  the  properties  of  the  compound.  This  is 
cited,  up  to  the  present,  as  a  fatal  objection  to  the  electro- 
chemical theory  of  Berzelius. 

The  very  recent  work  of  J.  J.  Thomson1  has,  however, 
thrown  entirely  new  light  on  the  above  line  of  argument. 
Thomson  has  shown  that  the  same  substance  may  be  both 
positively  and  negatively  charged.  Thus,  hydrogen  gas2 
has  been  electrolyzed  by  him,  with  the  result  that  positive 
hydrogen  went  to  one  pole  and  negative  to  the  other. 

i  Nature,  52,  453.  2  Ibid.,  52,  451  (1895). 


THE   EARLIER   PHYSICAL  CHEMISTRY  43 

This  was  shown  from  the  difference  in  the  spectra  of  the 
hydrogen  around  the  two  poles.  The  molecule  of  hydro- 
gen is,  then,  very  probably  made  up  of  a  positive  and  a 
negative  hydrogen  ion. 

The  important  point  in  this  connection,  brought  out  by 
the  work  of  Thomson,  is  that  we  must  not  conclude  that 
because  hydrogen  is  sometimes  positively  charged,  it  is 
always  so.  Thomson's  own  words,  in  connection  with  that 
portion  of  his  paper  which  bears  on  the  theory  of  Ber- 
zelius,  are  here  given. 

"  In  many  organic  compounds,  atoms  of  an  electroposi- 
tive element  hydrogen  are  replaced  by  atoms  of  an  elec- 
tronegative element  chlorine,  without  altering  the  type  of 
the  compound.  Thus,  for  example,  we  can  replace  the  4 
hydrogen  atoms  in  CH4,  by  Cl  atoms,  getting,  successively, 
the  compounds  CH3C1,  CH2C12,  CHC13,  and  CC14 :  it  seemed 
of  interest  to  investigate  what  was  the  nature  of  the  charge 
of  electricity  on  the  chlorine  atoms  in  these  compounds. 
The  point  is  of  some  historical  interest,  as  the  possibility 
of  substituting  an  electronegative  element  in  a  compound 
for  an  electropositive  one  was  one  of  the  chief  objections 
against  the  electrochemical  theory  of  Berzelius.  When  the 
vapor  of  chloroform  was  placed  in  the  tube,  it  was  found 
that  both  the  H  and  Cl  lines  were  bright  on  the  negative 
side  of  the  plate,  while  they  were  absent  from  the  positive 
side,  and  that  any  increase  in  the  brightness  of  the  H 
lines  was  accompanied  by  an  increase  in  the  brightness  of 
those  due  to  Cl.  .  .  .  The  appearance  of  the  H  and  Cl 
spectra  on  the  same  side  of  the  plate  was  also  observed  in 
methylene  chloride,  and  in  ethylene  chloride.  Even  when 
all  the  H  in  CH4  was  replaced  by  Cl,  as  in  carbon  tetra- 


44  ELECTROLYTIC  DISSOCIATION 

chloride  CC14,  the  Cl  spectra  still  clung  to  the  negative 
side  of  the  plate." 

The  same  point  was  tested  with  SiCl4,  and  the  Cl  spectra 
was  brightest  on  the  negative  side  of  the  plate.  "  From 
these  experiments  it  would  appear  that  the  Cl  atoms,  in 
the  chlorine  derivatives  of  methane,  are  charged  with  elec- 
tricity of  the  same  sign  as  the  H  atoms  they  displace." 

From  this,  the  argument  against  the  theory  of  Berzelius 
is  left  without  foundation,  since  the  hydrogen  atoms  in 
acetic  acid  are  replaced  by  chlorine,  which  has  the  same 
kind  of  charge.  Therefore,  the  properties  of  trichloracetic 
acid  should  resemble  closely  those  of  acetic  acid  itself. 

Faraday's  Law.  —  The  next  important  advance  in  elec- 
trochemistry was  made  by  Faraday,  upon  whose  investi- 
gations too  much  stress  cannot  be  laid.  He  showed  the 
identity  of  electricity  from  different  sources,  whether  pro- 
duced by  friction  or  by  chemical  action ;  and  also  investi- 
gated the  relation  between  the  amount  of  a  compound 
decomposed  by  the  current,  and  the  amount  of  current. 
He  found  that  the  two  were  proportional  to  one  another, 
and  then  announced  his  law. 

The  amount  of  chemical  decomposition  effected  by  the 
passage  of  the  current  is  proportional  to  the  amount  of 
electricity  which  flows  through  the  conductor. 

Faraday  determined,  also,  the  amounts  of  different  ele- 
ments, which  would  be  separated  from  their  compounds, 
by  passing  the  same  current  through  solutions  of  these 
compounds.  For  example,  the  same  current  would  be 
passed  through  solutions  of,  say,  copper  sulphate,  zinc 
chloride,  and  silver  nitrate,  and  the  amounts  of  Cu,  Zn,  and 
Ag  deposited  determined. 


THE   EARLIER   PHYSICAL  CHEMISTRY  45 

The  following  generalization  was  reached  by  this 
work :  — 

The  amounts  of  the  different  elements  which  are  sepa- 
rated by  the  same  quantity  of  electricity  bear  the  same 
relation  to  one  another  as  the  equivalents  of  these 
elements. 

The  atoms  of  all  univalent  elements  carry  exactly  the 
same  quantity  of  electricity,  —  of  bivalent  elements  twice  as 
much,  of  trivalent  three  times,  and  so  on.  In  a  word,  all 
atoms  have  either  the  same  capacity  for  electricity,  or  a 
simple  rational  multiple  of  the  capacity  of  the  univalent 
atoms. 

Faraday  is  also  the  author  of  the  system  of  nomencla- 
ture, which  we  use  in  electrochemistry  up  to  the  present. 

Electrolysis.  —  The  power  of  the  current  to  decompose 
chemical  compounds  had  been  made  especially  prominent 
by  the  work  of  Faraday.  This  he  termed  electrolysis. 

Some  of  the  most  interesting  and  important  advances 
made  in  electrochemistry,  at  that  time,  were  along  this  line ; 
and  theories  were  proposed  to  account  for  the  facts  then 
known,  which  we  now  recognize  to  contain  the  germ  of 
the  theory  of  electrolytic  dissociation.  If  the  two  poles 
of  a  voltaic  cell  are  immersed  in  acidulated  water,  hydro- 
gen is  liberated  upon  the  one  pole,  and  oxygen  upon  the 
other.  Between  the  two  poles  there  is  a  layer  of  water 
particles,  which  apparently  undergo  no  decomposition. 
The  question  arose,  do  the  hydrogen  and  oxygen  set  free, 
come  from  the  same  or  from  different  water  particles  ?  It 
is  not  a  simple  matter  to  answer  this  question  satisfac- 
torily, and  yet  it  is  fundamental  to  the  solution  of  the 
question  of  electrolysis. 


46  ELECTROLYTIC  DISSOCIATION 

A  superficial  examination  of  what  took  place  in  electroly- 
sis would  probably  lead  to  the  conclusion  that  the  hydro- 
gen and  oxygen  come  from  different  water  particles.  Yet 
it  might  be  that  the  water  which  was  decomposed  was 
that  which  was  exactly  halfway  between  the  poles,  and 
that  the  hydrogen  moved  from  this  point  in  the  one  direc- 
tion, and  the  oxygen  in  the  other. 

Humphry  Davy  undertook  to  answer  this  question  exper- 
imentally. He  placed  the  poles  of  a  voltaic  cell  in  sepa- 
rate vessels,  containing  acidulated  water,  and  connected  the 
two  vessels  by  placing  a  finger  of  one  hand  in  the  one, 
and  a  finger  of  the  other  hand  in  the  other,  care  being 
caken  to  properly  insulate  his  body  from  the  earth.  Elec- 
trolysis took  place,  hydrogen  separating  at  one  pole  of  the 
battery,  oxygen  at  the  other.  In  such  an  arrangement,  it 
;s  difficult  to  see  how  the  oxygen  and  hydrogen  set  free 
could  come  from  the  same  particle  of  water.  It  is,  there- 
fore, very  probable,  that  in  the  electrolysis  of  acidulated 
water,  the  hydrogen  and  oxygen  which  are  liberated  at 
the  poles  come  from  different  molecules  of  water. 

Theories  of  Electrolysis.  —  The  first  to  account  at  all 
satisfactorily  for  electrolysis  was  Grotthuss,  at  the  early 
date  of  1805.  At  the  moment  when  the  hydrogen  and 
oxygen  separate,  the  one  becomes  positive  and  the  other 
negative.  The  positively  charged  hydrogen  is  attracted 
to  the  negative  pole,  and  repelled  from  the  positive  pole. 
The  negatively  charged  oxygen  is  attracted  to  the  positive 
pole,  and  repelled  from  the  negative.  But  since  the  at- 
tracting and  repelling  forces  vary  inversely  as  the  square 
of  the  distance  from  the  electrodes,  the  sum  of  the  forces 
which  act,  respectively,  upon  the  hydrogen  and  oxygen 


THE   EARLIER   PHYSICAL  CHEMISTRY 


47 


particles,  as  they  approach  the  electrodes,  is  constan':. 
This  clear  and  concise  idea  of  Grotthuss  is  represented 
graphically  in  the  accompanying  figure. 

The  atoms  marked  positive  represent  hydrogen ;  those 
marked  negative,  oxygen.  Before  the  current  is  passed, 
each  oxygen  atom  is  combined  with  a  definite  hydrogen 
atom,  forming  water.  When  the  current  is  passed,  the 
hydrogen  atom  nearest  the  negative  pole  gives  up  its 
positive  charge  to  that  pole,  becoming  electrically  neutral, 
and  separates  as  hydrogen  gas.  The  oxygen  atom  which 


— 

± 

— 

+ 

— 

+ 

FIG.  i. 

was  originally  in  combination  with  this  hydrogen  is  now 
free,  but  it  combines  at  once  with  the  hydrogen  of  the 
next  molecule  of  water.  This  sets  another  oxygen  atom 
free,  which  combines  with  the  hydrogen  of  the  next  water 
molecule,  and  so  on  until  the  positive  pole  is  reached, 
when  the  last  oxygen  atom  in  the  chain,  not  finding  any 
hydrogen  with  which  to  combine,  takes  up  a  positive 
charge  from  the  positive  pole,  becomes  electrically  neutral, 
and  escapes  as  gaseous  oxygen. 

The  gases,  which  escape  only  at  the  electrodes,  come 


48  ELECTROLYTIC  DISSOCIATION 

from  different  molecules  of  water,  as  was  made  probable 
by  the  experiment  of  Davy.  The  layers  of  molecules 
between  the  electrodes  are,  during  the  electrolysis,  con- 
stantly interchanging  their  constituents. 

The  distinctive  feature  of  the  theory  of  Grotthuss  is, 
that  before  the  current  is  passed,  each  hydrogen  atom  is 
combined  fixedly  with  a  definite  oxygen  atom,  from  which 
it  never  parts  company.  The  current  must  first  decom- 
pose the  water  molecules,  before  any  electrolysis  can  take 
place.  This  theory  accounted,  satisfactorily,  for  all  the 
facts  which  were  known  about  electrolysis,  at  the  time 
when  it  was  proposed. 

Clausius'  Theory  of  Electrolysis.  —  While  the  theory  of 
Grotthuss  accounted  for  all  the  facts  which  were  then 
known,  new  facts  were  soon  brought  to  light,  which  could 
not  be  reconciled  with  it.  According  to  this  theory,  the 
current  must  first  decompose  the  molecules  before  it  can 
effect  any  electrolysis.  If  the  current  used  is  not  capable 
of  decomposing  one  molecule  of  water,  it  is  clear  that  it 
cannot  decompose  more  than  one,  and  no  electrolysis 
would  result.  But  as  the  strength  of  the  current  in- 
creases, it  must  reach  a  point  where  it  is  capable  of 
decomposing  a  molecule  of  water.  At  this  point  many 
molecules  must  be  simultaneously  decomposed,  since  they 
are  all  under  the  effect  of  the  same  force,  and  have  almost 
exactly  the  same  position  to  one  another.  If  the  con- 
ductor conducts  only  electrolytically,  we  must  conclude 
from  this  theory,  that  as  long  as  the  driving  force  in  the 
conductor  is  below  a  certain  limit,  no  current  will  pass ; 
but  when  it  has  reached  this  limit,  a  very  strong  current 
suddenly  exists. 


THE   EARLIER   PHYSICAL  CHEMISTRY  49 

Says  Clausius,1  this  conclusion  from  the  theory  is  in 
direct  opposition  to  what  are  now  known  to  be  the  facts. 
The  smallest  force  produces  a  current  by  alternate  de- 
composition and  reunion,  and  the  intensity  of  the  current 
increases  according  to  Ohm's  law,  i.e.  proportional  to 
the  force.  Therefore,  the  assumption  that  the  part  mole- 
cules of  an  electrolyte  are  combined  rigidly  to  form  whole 
molecules,  and  that  these  have  a  definite,  regular  arrange- 
ment, is  without  foundation. 

The  assumption,  then,  that  the  natural  condition  of  an 
electrolytic  liquid  is  one  of  equilibrium,  in  which  every 
positive  part  molecule  is  combined  rigidly  with  a  negative, 
was  abandoned  by  Clausius  as  untenable,  and  his  own. 
theory  proposed  in  its  place. 

An  electrolytic  solution  consists  mainly  of  whole  mole- 
cules of  the  electrolyte,  but  in  addition  there  are  some 
"  part  molecules,"  which  have  parted  co.mpany.  A  posi- 
tive part  molecule  may,  during  the  movements  to  which 
it  is  subjected,  come  into  a  position  with  respect  to  the 
negative  part  of  another  molecule,  which  is  more  favor- 
able for  union  with  this  than  with  its  own  negative  com- 
panion. It  would  then  part  company  with  the  latter,  and 
join  the  former.  This  would  have,  then,  a  positive  and  a 
negative  part  molecule,  each  free  -to  move  about  through 
the  solution  and  combine  with  other  part  molecules,  or 
break  down  whole  molecules  already  existing  as  such  in 
the  solution.  These  movements  and  decompositions  take 
place  as  irregularly  as  the  heat  movements  which  produce 
them.  The  two  part  molecules,  resulting  from  the  break- 
ing down  of  a  whole  molecule,  may  combine  directly  with 

1  Pogg.  Ann.,  loi,  338  (1857). 
E 


50  ELECTROLYTIC   DISSOCIATION 

one  another,  or  may  be  prevented  from  doing  so  by  the 
movements  due  to  heat.  The  amount  of  such  decompo- 
sition in  a  solution  would  depend  upon  the  nature  of  the 
solution  and  upon  the  temperature. 

Allow  an  electric  force  to  act  upon  a  solution  containing 
a  mixture  of  whole  and  of  part  molecules.  The  part  mole- 
cules will  no  longer  move  about  in  all  directions,  due  to 
the  action  of  heat  alone,  but  more  positive  parts  will  move 
in  the  direction  of  the  negative  pole,  and  negative  parts 
toward  the  positive  pole,  than  in  the  other  directions. 
This  directing  influence  of  the  current  will  also  facilitate 
the  breaking  down  of  the  whole  molecules  into  part 
molecules. 

This  assumption  of  a  partial  breaking  down  of  the  mole- 
cules in  an  electrolytic  solution,  before  the  current  is 
passed,  accounts  for  the  fact  that  a  weak  current  will  effect 
electrolysis — a  fact  which  could  not  be  brought  within  the 
range  of  the  theory  of  Grotthuss.  The  directing  influence 
which  the  current  exerts  would  exist  for  a  current  of  any 
strength,  and  would  be  proportional  to  the  strength  of  the 
current.  In  the  opinion  of  Clausius,  the  action  of  the 
current  is  primarily  a  directing  one,  but,  at  the  same  time, 
it  facilitates  the  decomposition  of  the  molecules  into  part 
molecules.  This  theory  of  Clausius,  as  will  be  seen  later, 
contains  the  germ  of  the  theory  of  electrolytic  dissociation. 

A  theory  as  to  the  condition  of  things  in  solution  was 
proposed  by  Williamson1  in  1851,  as  the  outcome  of  his 
work  on  the  preparation  of  ether  by  the  action  of  sulphuric 
acid  on  ethyl  alcohol.  The  reaction  which  produced  the 
ether  was  recognized  as  proceeding  in  two  stages :  — 

i  Liebig's  Ann.,  77,  45  (1851). 


THE  EARLIER   PHYSICAL  CHEMISTRY  51 

/OH  /OC2H5 

I.     S0<  +HOC2H5  =  S02<  +H20. 

X)H  \  OH 

<OC2H5  /OH          C2H5y 

-f  HOC2H5  =  SO2<;  +  >O. 

OH  X)H          C2U/ 

The  first  stage  of  the  reaction  consists  in  the  replacement 
of  a  hydrogen  atom  in  the  sulphuric  acid,  by  the  ethyl 
group,  with  the  elimination  of  a  molecule  of  water;  the 
second,  in  the  replacement  of  the  ethyl  group  in  ethyl  sul- 
phuric acid  by  the  hydroxyl  hydrogen  of  the  alcohol.  The 
reaction  which  takes  place  as  represented  in  I  is  then 
almost  exactly  reversed  in  II,  the  final  result  being  the 
removal  of  a  molecule  of  water  from  two  molecules  of 
alcohol,  and  the  formation  of  a  molecule  of  ether.  From 
this  Williamson  concluded,  "  that  in  an  aggregate  of  the 
molecules  of  every  compound,  a  constant  interchange 
between  the  elements  contained  in  them  is  taking 
place." 

He  concluded  his  paper  with  this  statement :  "  In  recent 
years  chemists  have  added  to  the  atomic  theory  an  uncer- 
tain, and,  as  I  believe,  an  unsubstantiated  hypothesis,  that 
the  atoms  are  in  a  condition  of  rest.  I  reject  this  hypothe- 
sis, and  found  my  views  on  the  broader  basis,  the  movement 
of  the  atoms."1 

Clausius  criticised  the  views  of  Williamson  as  being  too 
broad.  His  assumption  went  too  far  beyond  the  facts.  It 
was  not  necessary  to  assume  that  all,  or  even  a  large  part, 
of  the  molecules  in  a  solution  are  broken  down  into  part 

1  Liebig's  Ann.,  77,  48. 


52  ELECTROLYTIC  DISSOCIATION 

molecules.  The  assumption  that  a  few  of  the  molecules 
are  thus  broken  down,  accounted  for  all  the  facts  then 
known. 

Hittorf 's  Work  on  the  Migration  Velocity  of  Ions. — 
The  changes  in  concentration,  which  take  place  when 
solutions  are  electrolyzed,  could  be  explained  only  by 
assuming  that  the  positive  and  negative  part  molecules, 
or,  as  Faraday  called  them,  ions,  move  through  the  solu- 
tion with  different  velocities.  The  measurement  of  these 
relative  velocities  was  undertaken  by  Hittorf,1  and  his 
investigation  of  this  problem  has  now  become  a  classic. 
He  studied  the  effect  of  concentration  of  solution,  tempera- 
ture, and  strength  of  current,  upon  the  relative  velocities 
of  ions.  His  work  is  of  importance,  not  simply  as  giving 
us  the  relative  velocity  of  ions,  but  as  throwing  light  on  a 
number  of  other  problems.  What  ions  are  formed  from 
the  given  compounds  ?  which  constituents  go  to  make  up 
the  cation,  and  which  the  anion  ?  are  questions  which  come 
within  the  range  of  the  work  of  Hittorf.  Take  the  com- 
pound K2PtCl6 ;  does  the  platinum  form  part  of  the  ca- 
tion, or  of  the  anion  ?  does  it  go  to  the  positive  or  to  the 
negative  pole  ?  Or  take  the  compound  K4Fe(CN)6;  when 
it  is  electrolyzed,  does  the  iron  go  with  the  potassium  to 
the  cathode,  or  with  the  cyanogen  to  the  anode  ?  The 
solution  of  such  problems  is  of  great  assistance  in  deter- 
mining the  chemical  constitution,  especially  of  complex 
compounds. 

Kohlrausch's  Work  on  the  Conductivity  of  Solutions.  - 
Solutions  of  different  electrolytes  show  very  different  con- 
ducting power.     A  simple  and  accurate  method  of  meas- 

1  Pogg.  Ann.,  89,  117,  177 ;  98,  i ;  103,  i ;  106,  337,  513. 


THE  EARLIER  PHYSICAL  CHEMISTRY  53 

uring  the  conductivity  of  solutions  has  been  devised  by 
Kohlrausch.1  He  has  applied  his  method  to  a  large  num- 
ber of  solutions  of  different  concentrations  of  acids,  bases, 
and  salts ;  and  has  furnished  us  with  the  most  accurate 
conductivity  measurements  which  have  ever  been  made. 
The  results  of  this  work  will  be  considered  in  a  later 
chapter,  since  their  bearing  upon  the  theory  of  electro- 
lytic dissociation  is  direct.  Indeed,  we  shall  learn  that 
the  conductivity  of  solutions  of  electrolytes  furnishes  us 
with  one  of  the  most  rigid  tests  to  which  the  theory  of 
electrolytic  dissociation  can  be  subjected. 

THE   DEVELOPMENT  OF  CHEMICAL    DYNAMICS  AND   CHEMICAL 

STATICS 

The  brief  sketch  which  will  be  given  here,  of  the  de- 
velopment of  this  branch  of  physical  chemistry,  will  not 
include  the  earliest  suggestions  to  account  for  chemical 
action,  since  many  of  them  are  now  only  of  historical 
interest.  The  Swedish  chemist,  Bergmann,  attempted 
generalizations  which  were  undoubtedly  advances  on  the 
disconnected  knowledge  before  his  time;  but  it  was 
Wenzel  (1777)  who  first  saw  clearly  the  effect  of  mass 
on  chemical  action,  and  laid  the  foundation  for  the  law  of 
mass  action,  which  has  played  such  a  prominent  role  since 
his  time.  He,  however,  gave  only  a  qualitative  expression 
to  the  law;  viz.,  that  chemical  action  is  proportional  to 
the  concentration  of  the  substances  which  are  allowed  to 
react. 

Berthollet   developed    much   more   fully   the   effect   of 

1  Pogg.  Ann.,  138,  380;  IV,  i;  159,233;  Wie4.  Ann.,  6,  i ;  11,653;  2<5,  161. 


54  ELECTROLYTIC  DISSOCIATION 

mass  in  chemical  action,  and  showed  by  direct  experi- 
ment how  it  comes  into  play.  The  affinities  which  exist 
between  substances  are  not  to  be  regarded  as  absolute 
forces,  but  are  dependent  upon  the  masses  of  the  sub- 
stances which  are  present.  Thus  barium  sulphate  can  be 
partly  decomposed  by  boiling  it  with  potassium  hydroxide. 
Calcium  oxalate  can,  similarly,  be  partly  decomposed  by 
the  same  reagent.  If  the  potassium  hydroxide  is  present 
only  in  small  quantity,  no  appreciable  decomposition  takes 
place;  but  if  the  quantity  is  large,  and  is  removed  from 
time  to  time,  new  alkali  being  added,  barium  sulphate 
can  be  completely  decomposed  by  boiling  potassium  hy- 
droxide. This  was  a  clear  demonstration  of  the  effect  of 
mass. 

Following  this  same  idea,  Berthollet  pointed  out  the 
effect  of  the  state  of  aggregation  on  chemical  activity. 
That  chemical  activity  should  be  greatest,  it  is  necessary 
that  all  the  parts  should  come  into  action.  This  is  best 
effected  in  the  liquid  state  of  aggregation.  If  a  solid  is 
present,  the  activity  is  less,  or  if  a  solid  is  formed  as  the 
result  of  the  reaction,  its  activity  is  far  less  than  in  the 
liquid  condition.  Similarly,  if  a  gas  is  formed  in  the  reac- 
tion, it  quickly  escapes  from  the  field  of  action,  and  its 
chemical  activity  therefore  ceases. 

This  work  of  Berthollet  was  published  in  two  volumes 
as  his  "  Essai  de  Statique  Chimique,"  but  was  so  far  in 
advance  of  its  day,  that  it  either  failed  to  attract  attention 
altogether,  or  only  aroused  opposition  from  those  who  did 
not  comprehend  its  full  significance. 

It  was  much  later  before  any  further  evidence  was 
brought  forward,  to  show  the  effect  of  mass  in  chemical 


THE  EARLIER  PHYSICAL  CHEMISTRY  55 

activity.  Heinrich  Rose1  showed  that  the  sulphides  of 
the  alkaline  earths  are  largely  decomposed  when  boiled 
with  large  volumes  of  water,  liberating  hydrogen  sulphide, 
and  forming  the  hydroxide. 

He  also  called  attention  2  to  a  process  which  is  going  on 
in  nature.  Over  the  surface  of  the  earth  the  weak  chemi- 
cal reagents,  carbon  dioxide  and  water,  are  continually 
decomposing  some  of  the  most  stable  compounds  —  the 
silicates.  The  geological  process  known  as  weathering  is 
a  replacement  of  silicates  by  hydroxides  and  carbonates, 
or  by  basic  carbonates.  This  reaction,  in  which  such 
stable  compounds  are  broken  down  by  such  a  weak  acid 
as  carbonic  acid,  requires,  of  course,  a  long  period  of  time, 
and  is  the  result  of  the  mass  action  of  a  large  amount  of 
carbon  dioxide,  such  as  exists  in  the  atmosphere,  and  in 
the  soil.  Such  a  reaction  is  entirely  beyond  the  possi- 
bilities of  the  laboratory,  on  account  of  the  time  and  mass 
of  substance  required  to  effect  it. 

Rose  3  also  carried  out  some  investigations  on  the  decom- 
position of  insoluble  salts  by  soluble  salts.  It  was  known, 
long  before  his  time,  that  barium  sulphate  can  be  trans- 
formed into  the  carbonate,  both  by  fusion  with  potassium 
carbonate,  and  also  by  boiling  with  an  aqueous  solution  of 
potassium  carbonate.  Rose,  however,  undertook  a  quan- 
titative study  of  the  conditions  under  which  this  transfor- 
mation takes  place,  and  the  amount  of  carbonate  required 
to  effect  complete  decomposition.  He  found  that  the  sul- 
phates of  strontium  and  calcium  are  more  easily  decom- 
posed by  alkaline  carbonates  than  the  sulphate  of  barium, 

1  Pogg.  Ann.,  55,  415.  2  /^v/.,  82,  545. 

»  Ibid.,  94,  481 ;  95,  96,  284,  426. 


56  ELECTROLYTIC  DISSOCIATION 

and  concluded,  correctly,  that  this  was  due  to  the  presence 
of  a  reversible  reaction  between  the  barium  carbonate  and 
alkaline  sulphate  formed,  resulting  in  the  reformation  of 
barium  sulphate. 

The  result  of  this  work  of  Rose,  and  that  of  his  con- 
temporaries, was  to  call  attention  to  the  role  played  by 
mass  in  bringing  about  chemical  reaction.  The  full  im- 
portance of  the  action  of  mass,  as  we  shall  see,  was,  how- 
ever, not  recognized  until  somewhat  later. 

Wilhelmy 's  Discovery  of  the  Law  of  Reaction  Velocity.  — 
Wilhelmy l  treated  cane-sugar  with  a  number  of  acids,  and 
studied  the  velocities  with  which  inversion  takes  place. 
He  worked  with  different  acids,  with  different  amounts  of 
cane-sugar,  and  at  different  temperatures.  He  found  that 
it  was  only  the  sugar  which  underwent  change,  the  acid 
remaining  unaltered.  The  law  of  mass  was  found  to 
obtain ;  the  amount  of  sugar  transformed  in  a  given  time 
being  proportional  to  the  amount  present  at  that  time. 

Applying  the  principle  of  mass,  —  remembering  that  it 
is  only  the  sugar  which  undergoes  change,  the  acid  being 
unaltered, — Wilhelmy  deduced  the  following  mathemat- 
ical relations,  which  are  taken  from  his  epoch-making 
paper:2  — 

"  Let  dZ  be  the  amount  of  sugar  inverted  in  unit  time 
dT,  and  let  us  assume  that  this  is  determined  by  the 
formula : l  — 

I         |  ,  ..'     -fT=MZS 

in  which  M  is  the  mean  value  of  the  infinitely  small  quan- 
tity of  sugar,  which  is  transformed  in  unit  time,  by  the 

1  Pogg.  Ann.,  81,  413  (1850).  2  Ibid.,  81,  418. 


THE   EARLIER   PHYSICAL  CHEMISTRY  57 

action  of  the  unit  of  acid  present.     (Z  is  the  amount  of 
the  sugar,  5  that  of  the  acid.) 

"  The  above  equation  gives,  on  integration  :  — 


or  since,  as  already  shown,  J?  is  constant,  M  is  also  inde- 
pendent of  Z,  and  at  the  same  time  of  T,  which  should 
be  proved  later  by  experiment  :  — 

LogZ  =  -  MST+  C. 
For  T  =  o,  Z  —  Z0,  whence  : 
Log  Z§  —  log  Z  =  MS  T,  or  Z  = 


Since  Z^  S,  and  T  are  given,  and  Z  is  known  by  experi- 
ment, the  formula  can  be  used  to  determine  M" 

This  work  of  Wilhelmy,  which  must  be  regarded  as  the 
foundation  of  chemical  dynamics,  like  most  important  inves- 
tigations, did  not  receive  a  just  recognition  until  attention 
was  called  to  it  much  later.1  When  we  consider  that  this 
was  the  first  successful  attempt  to  express  the  velocity  of 
a  chemical  reaction  mathematically,  and  that  this  was  in 
1850,  we  can  form  some  conception  of  the  rapidity  of  the 
growth  of  knowledge  along  this  line. 

Other  contributions  to  our  knowledge  of  the  mechanism 
of  chemical  reactions  were  made  in  the  next  few  years. 
Lowenthal  and  Lenssen  2  showed  that  the  amount  of  sugar 
inverted  by  different  acids  was  proportional  to  the  strength 
of  the  acids.  But  the  next  marked  advance  we  owe  to  the 
French  chemist  Berthelot. 

1  Ostwald,  Journ.  prakt.  Chem.,  29,  385  (1884). 

2  Journ.  prakt.  Chem.,  85,  321  (1852). 


58  ELECTROLYTIC   DISSOCIATION 

Work  of  Berthelot  and  P6an  de  St.  Gilles.  —  Berthelot 
and  Pean  de  St.  Gilles1  made  an  elaborate  investigation 
of  the  conditions  of  formation  and  decomposition  of  ethe- 
real salts.  The  reactions  by  which  these  are  formed  from 
acids  and  alcohols  proceed  slowly,  and  tend  toward  a  limit, 
the  point  at  which  the  reaction  reaches  a  condition  of 
equilibrium  depending  upon  the  amount  of  acid  or  alcohol 
present,  upon  the  temperature,  etc.  On  the  other  hand, 
if  an  ethereal  salt  is  treated  with  water,  a  certain  amount 
of  it  is  decomposed,  the  amount  depending  upon  the  quan- 
tity of  water  used,  and  other  conditions.  A  reaction  of  this 
kind  is,  evidently,  well  adapted  to  the  study  of  reaction 
velocity,  condition  of  equilibrium,  etc. 

They  determined  the  effect  of  temperature  on  the 
velocity  of  this  reaction,  and  found  that  to  transform  30 
per  cent  of  a  given  mixture  of  alcohol  and  acid,  at  from 
6°  to  9°,  required  95  days,  while  at  100°  it  required  less 
than  5  hours  to  effect  the  same  transformation.  Pressure 
was  found  to  have  no  influence  on  reaction  velocity,  at 
least  up  to  sixty  or  eighty  atmospheres. 

Berthelot2  and  St.  Gilles,  in  the  course  of  their  study 
of  ether  formation,  arrived  at  the  following  generalization  : 
"  The  amount  of  ether  formed  in  every  moment  is  pro- 
portional to  the  product  of  the  reacting  substances." 
This  was  a  beautiful  confirmation  of  the  action  of  mass. 

They  also  determined  the  relation  between  chemical 
composition  and  the  amount  of  ether  formed.  A  few  of 
their  results  are  given,  using  different  alcohols  and  acids, 
and  allowing  the  reaction  to  proceed  until  equilibrium  was 

1  Ann.  Chim.  Phys.  [3] ,  65, 385 ;  66,  5 ;  68,  225  (1862-1863). 

2  Ibid.  [3],  68,  225. 


THE  EARLIER  PHYSICAL  CHEMISTRY  59 

reached,  i.e.  until  the  maximum  amount  of  ether  was 
formed  under  the  conditions.  This  is  indicated  in  per- 
centage of  the  theoretical  amount  of  ether  which  might 
be  formed  under  the  conditions,  if  the  reaction  went  to 
the  end. 

LIMIT 

C2H6O  withCH3COOH  66.9% 

C2H6O  with  CH3  -  CH2  -  CH2  •  COOH  69.8% 

C2H6O  with  C6H5COOH  67.0%  ' 

CH4O    withCH3COOH  67.5% 

CH4O    withC6H5COOH  64.5% 

CH4O    with  C2H4(COOH)2  66.1% 

C5H120  with  CH3COOH  68.9% 

CgH^O  with  CH3  •  CH2  •  CH2  •  COOH  70.7% 

CgH^O  with  C6H5COOH  70.0% 

This  is  a  remarkable  result.  Neither  the  chemical  com- 
position of  the  acid,  nor  of  the  base,  has  any  marked 
influence  on  the  amount  of  ether  formed. 

The  effect  of  increasing  the  amount  of  the  alcohol,  with 
respect  to  the  acid,  was  also  determined. 

n  is  the  number  of  equivalents  of  ethyl  alcohol,  to  one 
equivalent  of  acetic  acid. 

n         LIMIT  n  LIMIT  «  LIMIT 

0.2       19.3%  2.         82.8%  12.0      93-2% 

0.5     42.0%  4.       88.2%  19.0     95.0% 

i.o     66.5%  5.4     90.2%  50.0  100.0% 

i-5     77-9% 

These  results  exhibit  the  effect  of  mass  in  a  striking 
manner ;  all  the  acid  being  transformed  into  ethereal  salt, 
when  fifty  equivalents  of  alcohol  are  present  to  one  of  acid. 

The  action  of  mass  was   shown  also   by  the  work  of 


60  ELECTROLYTIC  DISSOCIATION 

Deville  1  on  dissociation.  Many  substances  are  partially 
broken  down  by  heat  into  their  constituents  —  in  many 
cases  into  their  elements.  Thus,  water-vapor  at  a  high  heat 
is  partially  decomposed  into  hydrogen  and  oxygen.  The 
fact  was  established,  that  if  either  the  hydrogen  or  oxygen 
resulting  from  the  decomposition  is  removed,  the  dissocia- 
tion will  proceed  farther,  and  may  become  complete.  If, 
on  the  other  hand,  an  excess  of  either  hydrogen  or  oxygen 
is  added  to  the  dissociating  water-vapor,  the  amount  of 
dissociation  is  decreased.  Deville  studied  a  number  of 
cases,  and  concluded  that  this  is  general,  that  an  excess 
of  either  of  the  products  of  dissociation  will  diminish 
the  amount  of  dissociation  of  a  vapor.  An  excellent  ex- 
ample of  this  is  furnished  by  phosphorus  pentachloride. 
This  compound  cannot  be  volatilized  without  decomposi- 
tion, unless  there  is  an  excess  of  either  chlorine  or  phos- 
phorus trichloride  present.  In  the  presence  of  an  excess 
of  one  of  these,  the  molecular  weight  of  phosphorus  penta- 
chloride, as  determined,  is  very  close  to  the  theoretical 
molecular  weight. 

This  work  of  Deville  is  one  of  the  most  direct  confirma- 
tions of  the  effect  of  mass,  yet  it  was  used  by  him  as  an 
argument  against  mass  action,  being  a  factor  in  chemical 
activity.  Another  example  of  admirable  work,  but  erro- 
neous interpretation  of  results  obtained. 

Guldberg  and  Waage's  Law  of  Mass  Action.  —  We  have 
seen  that  the  effect  of  mass  on  chemical  activity  was 
recognized  as  early  as  the  time  of  Wenzel.  A  clearer 
expression  of  its  action  was  furnished  by  Berthollet.  Rose 
showed,  both  from  nature,  and  by  direct  experiment,  what 

1  Compt.  rend.,  45,  857 ;  56,  195,  729 ;  59,  873 ;  60,  317. 


THE  EARLIER   PHYSICAL  CHEMISTRY  6 1 

a  marked  influence  mass  has  in  effecting  chemical  reac- 
tions. Berthelot  and  Pean  de  St.  Gilles  demonstrated  the 
effect  of  mass  action  on  the  formation  of  ethereal  salts 
from  alcohols  and  acids,  and  thus  made  it  probable  that 
the  effect  of  mass  on  chemical  reactions  is  general. 

It  was  Guldberg  and  Waage,1  however,  who  gave  a  com- 
plete mathematical  expression  to  the  action  of  mass.  If 
two  substances  react,  the  action  is  proportional  to  the  active 
masses  of  each  of  them.  The  intensity  of  the  reaction  is, 
therefore,  measured  by  the  product  of  the  active  masses. 
The  reaction  is,  of  course,  dependent  also  upon  the  nature 
of  the  substances,  temperature,  etc.  These  must  be  taken 
into  account.  If  we  represent  the  active  masses  of  two 
substances  by  m  and  n,  and  the  coefficient  depending  upon 
the  nature  of  the  substance,  etc.,  by  c,  the  force  of  the 
chemical  reaction  is  expressed  by  mnc. 

If  the  reaction  is  reversible,  i.e.  if  the  substances  formed 
can  react  and  give  the  original  substances,  as  e.g.  in  the 
formation  of  ethereal  salts,  then  there  will  exist  a  force 
which  tends  to  stop  the  original  reaction,  and  to  set  up 
one  in  exactly  the  opposite  sense.  If  we  represent  the 
active  masses  of  the  substances  formed  in  the  original 
reaction  by  m'  and  n* ',  and  the  coefficient  depending  upon 
the  nature  of  the  substances  by  cf,  the  magnitude  of  the 
force  opposing  the  original  reaction  will  be  expressed  by 
m'n'c'. 

When  the  condition  of  equilibrium  is  reached,  the  two 
forces  are  equal  and  opposite,  and  we  have :  — 

mnc  =  m'n'c1 (i) 

1  fetudes  sur  les  Affinit6s  Chimiques,  Christiania,  1867 ;  Journ.  prakt.  Chem.  [2], 
19,  69  (1879).  Ostwald's  Lehrb.  d.  allg.  Chemie,  II,  2,  p.  104. 


62  ELECTROLYTIC  DISSOCIATION 

If  we  bring  together  equivalents  of  the  four  substances 
m,  n,  m1 \  n* ',  they  will  generally  not  be  in  a  state  of  equilib- 
rium, but  a  certain  amount  of  m  and  n  will  pass  over  into 
m1  and  n1 ,  and  this  amount  we  will  call  x.  The  amounts 
of  the  four  substances  present  will  then  be,  m  —  x,  n  —  x, 
m'  +  x,  nr  +  x.  The  active  masses  being  the  amounts  in 
a  given  volume  vt  we  will  have  :  — 

m  —  x    n  —  x    m'  +  x    n1  +  x 

V  V  V  V 

where  v  is  the  entire  volume  of  the  solution.  Substituting 
these  values  for  m,  n,  mf,  and  n'  in  (i),  we  have :  — 

(m  -x)(n-  x)  =  ^<>'  +  *)(»'  +  *). 
k 

This  equation  is  perfectly  general,  applying  to  all  values 

of  x.     If  we  determine  x  in  any  one  case,  we  can  calculate 

k'  k' 

—     Knowing  — ,we  can  calculate  the  value  of  x  for  any 

k  k 

amounts  of  the  original  substances  brought  together.  In 
a  word,  we  could  calculate  exactly  how  the  four  substances 
would  react,  whatever  the  quantities  brought  together,  and 
how  much  of  each  would  exist  when  equilibrium  was 
reached. 

Guldberg  and  Waage's  work  also  led  to  a  more  com- 
prehensive conception  of  the  reversibility  of  many  chemi- 
cal reactions,  equilibrium  being  the  special  condition 
under  which  the  reactions  in  the  two  directions  were  of 
equal  velocity.  The  velocity  of  any  reaction  is,  in  reality, 
the  difference  between  the  velocity  in  one  direction,  and 
the  velocity  in  the  other.  The  velocity  v  is  the  amount 

transformed  in  unit  time,  v  =  — ^ ;  but  this  is  equal  to  a 

dT 


THE   EARLIER   PHYSICAL   CHEMISTRY  63 

factor  0  times  the  force  acting  in  one  direction,  minus  the 
force  acting  in  the  other  direction. 

v  ='  —  ±;  =  0(mnc  —  mfnfcf). 

If  the  reaction  proceeds  only  in  one  direction,  m'n'c1  be- 
comes equal  to  zero,  and  the  equation  of  reaction  velocity 
becomes  :  — 


The  above  relations  obtain,  only  when  all  of  the  sub- 
stances which  enter  into  the  reaction  are  soluble.  If  one 
or  more  of  the  substances  is  insoluble,  the  relations  are 
much  simplified.  Take  the  reaction  between  potassium 
carbonate  and  barium  sulphate,  in  which  potassium  sul- 
phate and  barium  carbonate  are  formed. 

Let  M  be  the  active  mass  of  potassium  carbonate. 

Let  N  be  the  active  mass  of  barium  sulphate. 

Let  M'  be  the  active  mass  of  potassium  sulphate. 

Let  N'  be  the  active  mass  of  barium  carbonate. 

Barium  sulphate  and  barium  carbonate  are  insoluble, 
and  their  active  masses,  N  and  N',  are,  therefore,  con- 
stant. We  have  then  :  — 

MC=M'C'  or  Jp  =  constant 

This  is  a  very  simple  relation,  and  holds  whenever  two 
of  the  substances  are  insoluble.  The  value  of  the  con- 
stants for  the  insoluble  substances  depends  upon  their 
degree  of  insolubility. 

The  law  of  mass  action  has  been  tested  in  a  large  num- 
ber of  directions,  and  by  a  great  variety  of  methods.  The 


64  ELECTROLYTIC   DISSOCIATION 

general  result  has  been  a  thorough   confirmation  of   the 
views  of  Guldberg  and  Waage. 

The  Application  of  Thermodynamics  to  Chemical  Pro- 
cesses. —  The  scope  of  this  work  will  not  permit  of  more 
than  a  brief  reference  to  the  leading  investigations  bearing 
upon  this  problem.  Horstmann  :  was  the  first  to  success- 
fully apply  thermodynamics  to  chemical  processes.  He 
chose  dissociation  phenomena,  since  they  are  reversible 
processes  ;  and  if  they  take  place  between  solids  and  gases, 
obey  the  same  laws  as  vaporization.  If  we  represent  by 
//  the  heat  of  combination,  and  by  /  the  dissociation  press- 
ure, the  following  relation  between  the  two  obtains  :  — 


in  which  T  is  the  absolute  temperature,  and  u  the  volume 
of  the  vapor.  Knowing  either^  or/,  we  can  calculate  the 
other.  He  later  applied  the  entropy  principle  to  conditions 
of  equilibrium,  and  showed  that  a  system  will  always 
assume  that  arrangement  in  which  entropy  is  a  maximum. 
The  condition  for  equilibrium  is  then  :  — 

*-* 

dx 

in  which  e  is  the  entropy,  and  x  the  amount  of  untrans- 
formed  substance. 

Willard  Gibbs's2  applications  of  thermodynamics  to  con- 
ditions of  chemical  equilibrium  are  so  comprehensive  and 
general,  that  it  is  impossible  to  give  any  adequate  concep- 

1  Ber.  d.  chem.  Gesell.,  2,  137;  4,  635;  Liebig's  Ann.,  170,  192  (1872-1873). 

2  Trans.  Conn.  Acad.,  Ill,  1874-1878.    Translated  into  German  by  Ostwald, 
Leipzig,  1892. 


THE   EARLIER   PHYSICAL  CHEMISTRY  65 

tion  of  his  epoch-making  work  in  a  few  paragraphs.  The 
reader  who  may  desire  to  follow  out  Gibbs's  mathematical 
deductions  must  be  referred  to. his  original  communication, 
or  to  the  second  part  of  the  second  volume  of  Ostwald's 
Lehrbuch,  where  a  systematic  account  of  his  deduction  is 
given. 

It  should,  however,  be  stated  here,  that  the  work  of 
Willard  Gibbs  has  placed  the  science  of  chemical  equilib- 
rium on  an  entirely  new  basis,  from  the  theoretical  stand- 
point, and  is  ranked  as  one  of  the  leading  contributions  to 
mathematical  chemistry  and  physics. 

The  work  of  van't  Hoff:1  is  in  part  theoretical,  and  in 
part  experimental.  This  deals  largely  with  the  velocity 
of  reactions  from  both  standpoints,  and  also  investigates 
the  influences  which  affect  the  velocity  of  a  reaction,  such 
as  temperature,  pressure,  form  of  vessel,  etc.  The  con- 
ditions of  equilibrium  were  also  investigated  by  van't  Hoff 
and  his  pupils,  and  the  temperatures  ascertained  at  which 
a  large  number  of  transformations  take  place. 

The  observations  for  the  different  kinds  of  equilibrium 
have  led  to  the  following  general  conclusion : 2  "  Every 
equilibrium  between  two  different  conditions  of  matter 
(systems)  is,  at  constant  volume,  by  a  decrease  in  temper- 
ature, displaced  in  the  sense  of  that  system  whose  forma- 
tion liberates  heat."  This  generalization  includes  all  pos- 
sible cases  of  chemical  as  well  as  of  physical  equilibrium. 
This  principle,  termed  by  van't  Hoff  that  of  "movable 
equilibrium,"  is  then  applied  to  both  heterogeneous  and 

1  Etudes  de  Dynamique  Chimique,  Amsterdam,  1884.    Studien  zur  Chemischen 
Dynamik,  van't  Hoff  and  Cohen. 

2  Studien  zur  Chemischen  Dynamik  (van't  Hoff  and  Cohen),  p.  223. 

F 


66  ELECTROLYTIC  DISSOCIATION 

homogeneous  equilibria.  The  concluding  chapter  of  this 
important  work  by  van't  Hoff  and  Cohen  is  devoted  to 
the  subject  of  chemical  affinity.  The  generalization  reached 
was,1  that  "  the  work  expressed  in  calories,  which  affinity 
can  do  in  a  chemical  transformation,  at  a  given  tempera- 
ture, is  equal  to  the  amount  of  heat  which  this  transforma- 
tion produces,  divided  by  the  absolute  temperature  at 
which  the  transformation  takes  place,  and  multiplied  by 
the  difference  between  this,  and  the  temperature  at  which 
the  transformation  takes  place." 

If  A  is  the  amount  of  work  done,  q  the  amount  of  heat 
produced,  T  the  temperature  of  the  transformation,  and 
P  the  absolute  temperature  of  the  transformation,  we 

have : — 

A=    (P-T\ 


which  is  the  mathematical  expression  of  the  above  gener- 
alization. In  connection  with  the  study  of  chemical  equi- 
librium, the  work  of  Le  Chatelier2  must  be  mentioned. 
He  arrived  at  two  laws  which  he  stated  thus :  Law  of  the 
opposition  of  action  and  reaction  (page  210).  "Every 
variation  of  a  factor  of  equilibrium  causes  a  transformation 
of  the  system,  which  tends  to  make  the  factor  in  question 
undergo  a  variation  of  sign  opposite  to  that  which  we  have 
given  it." 

Thus,  an  elevation  of  temperature  produces  a  reaction 
with  absorption  of  heat,  an  increase  in  pressure  a  reaction 
with  diminution  of  volume,  etc. 

1  Studien  zur  Chemischen  Dynamik,  p.  247. 

2  Recherches  Exp6rimentales  et  Th6oriques  sur  les  Equilibres  Chimiques.    Paris, 
1888. 


THE   EARLIER   PHYSICAL  CHEMISTRY  67 

Le  Chatelier  termed  his  second  generalization  the  law 
of  equivalence  of  systems  in  equilibrium,  and  expressed  ijt 
thus :  - 

"Two  equivalent  elements  in  a  system  in  equilibrium, 
i.e.  which  can  be  substituted  for  one  another  without  chang- 
ing the  condition  of  equilibrium,  will  be  equivalent  in  every 
other  system  where  they  can  be  substituted  for  one  another, 
and  further,  will  be  mutually  in  equilibrium  if  in  opposition 
to  one  another." 

An  example  cited  is  the  equality  of  the  vapor-tension  of 
water  and  of  ice  at  the  melting-point. 

Methods  of  measuring  Affinity.  —  The  theoretical  deduc- 
tions, especially  of  the  last  four  pieces  of  work  referred  to, 
have  been  tested  experimentally  by  a  number  of  methods. 
Julius  Thomsen  *  determined  the  way  in  which  a  base  is 
divided  between  two  acids,  by  means  of  the  amount  of  heat 
liberated.  While  Ostwald,2  utilizing  the  change  in  volume 
which  occurs  in  chemical  reactions,  obtained  far  more 
satisfactory  and  reliable  results  than  Thomsen.  Ostwald 
showed  that  the  action  between  acids  and  bases  is  condi- 
tioned by  two  coefficients,  the  one  depending  upon  the 
nature  of  the  acid,  the  other  upon  the  nature  of  the  base. 
The  chemical  affinity  of  an  acid  for  a  base  is  then  expressed 
by  the  product  of  these  two  coefficients.  These  affinity 
coefficients  are  the  numerical  expressions  of  the  strength 
of  the  acid  or  base,  and  hold,  quantitatively,  for  all  actions 
in  which  the  acid  or  base  takes  part. 

In  addition  to  the  thermochemical  method  of  J.  Thom- 
sen, and  the  simpler  and  more  reliable  volume  chemical 

1  Pogg.  Ann.,  138,  497  (1869). 

2  Journ.  prakt.  Chem.  [2],  16,  385  (1877). 


68  ELECTROLYTIC  DISSOCIATION 

method  of  Ostwald,  a  number  of  other  methods  of  measur- 
ing relative  affinities  have  been  devised.  Ostwald1  pro- 
posed the  velocity  with  which  substances  like  zinc  sulphide, 
or  calcium  oxalate,  are  dissolved  by  different  acids,  as  a 
measure  of  the  relative  affinities  of  the  acids.  He2  also 
used  the  velocity,  with  which  a  reaction  like  the  transfor- 
mation of  acetamid  into  ammonium  acetate  takes  place 
under  the  influence  of  acids,  as  a  measure  of  the  affinities 
of  the  acids.  Ostwald  has  also  studied  other  reactions  in 
this  same  connection,  such  as  the  catalysis  of  methyl 
acetate,  inversion  of  cane-sugar,  etc.,  and  found  that  the 
coefficients  for  the  different  acids,  as  determined  by  the 
different  methods,  agreed  satisfactorily. 

A  relation  was  thus  discovered,  which,  as  we  will  see,  is 
of  the  very  greatest  importance,  in  connection  with  the 
theory  of  electrolytic  dissociation.  The  affinity  coefficients 
of  acids  and  bases  bear  the  same  quantitative  relations  to 
one  another  as  the  conductivities  of  these  acids  and  bases. 

The  discussion  of  this  relation  belongs  to  a  later  chapter 
of  this  work,  and  it  suffices  here  to  merely  call  attention 
to  its  existence. 

Conclusions  from  the  Earlier  Physical  Chemical  Work.  — 
From  the  preceding  sketch  of  the  development  of  the 
several  chapters  of  physical  chemistry,  we  can  form  .a 
fairly  clear  conception  of  the  state  of  physical  chemistry 
just  before  the  theory  of  electrolytic  dissociation  was 
proposed.  Much  work  had  been  done  on  the  relations 
between  the  various  properties,  and  composition  and  con- 
stitution ;  and  a  great  number  of  generalizations  had  been 
reached,  which,  however,  held  only  approximately.  Much 

1  Journ.  prakt.  Chem.  [2],  19,  468  (1879).  2  -^"^  [2L  27»  x  (I88s). 


THE   EARLIER   PHYSICAL  CHEMISTRY  69 

valuable  experimental  work  had  also  been  done  on  the 
amount  of  heat  liberated  in  chemical  reactions,  laying 
stress  upon  the  energy  transformations  which  take  place 
in  chemical  processes,  and  which  are  probably  the  condi- 
tioning causes  of  all  chemical  action.  Here,  also,  relations 
were  pointed  out,  which,  however,  like  the  above,  have 
been  shown  to  be  only  approximations.  Then,  the  founda- 
tions of  electrochemistry  were  laid,  early  in  the  century, 
and  rapidly  developed,  and  theories  to  refer  chemical 
action  to  purely  electrical  causes  were  proposed.  The 
decomposing  action  of  the  current  was  studied,  and  theo- 
ries advanced  to  explain  electrolysis,  which  lie  at  the 
foundation  of  our  most  modern  theory.  The  relation 
pointed  out  here  by  Faraday,  between  the  amount  of 
current  and  the  amount  of  decomposition  which  it  effects, 
is  one  of  the  most  exact  with  which  we  have  to  deal. 
Similarly,  other  electrochemical  relations  are  freer  from 
exceptions  than  those  which  we  have  just  considered. 
Some  of  the  more  important  steps  in  the  development  of 
chemical  dynamics  and  statics  have  been  taken  up,  includ- 
ing, especially,  the  law  of  mass  action,  which  underlies  this 
entire  chapter  of  physical  chemistry. 

But,  from  what  has  preceded,  we  can  see  not  only 
the  state  of  development,  but  also  the  inherent  nature 
of  physical  chemistry.  What  was  the  chief  aim  of  the 
physical  chemist  in  these  earlier  periods  ?  It  was,  plainly, 
to  discover  relations  between  apparently  disconnected 
phenomena  and  disconnected  facts.  It  attempted  to  con- 
nect, and  thus  systematize,  the  great  masses  of  isolated 
facts,  which  were  yearly  being  brought  to  light,  and  thus 
refer  them,  as  far  as  possible,  to  common  causes. 


/O  ELECTROLYTIC  DISSOCIATION 

It  has,  however,  been  repeatedly  shown,  that  these  earlier 
relations  were,  in  many  cases,  only  approximations.  The 
number  of  exceptions  continued  to  increase,  as  more  ac- 
curate experimental  work  was  done,  until,  in  some  cases, 
the  generalization  almost  entirely  disappeared.  Neverthe- 
less, the  aim  of  the  earlier  physical  chemist  is  the  aim  of 
the  physical  chemist  of  to-day  —  to  discover  generalizations 
wherever  they  exist.  It  is  by  this  means,  and  this  means 
only,  that  chemistry  can  be  advanced  from  pure  empiri- 
cism to  the  rank  of  an  exact  mathematical  science. 

We  will  now  follow  the  rise  and  development  of  the 
widest  and  most  important  generalization  which  has  ever 
been  reached  by  physical  chemistry. 


CHAPTER   II 

THE  ORIGIN  OF  THE  THEORY  OF  ELECTROLYTIC 
DISSOCIATION 

PFEFFER'S  OSMOTIC  INVESTIGATIONS 

Introduction. — If  we  would  trace  the  origin  of  the 
theory  of  electrolytic  dissociation,  we  must  turn  neither  to 
chemistry  nor  to  physics,  but  to  the  osmotic  investigations 
of  the  botanist,  W.  Pfeffer.1  It  had  long  been  known, 
that  when  a  solution  of  a  substance  is  placed  upon  one 
side  of  a  partition,  through  which  the  solvent  can  pass 
but  the  dissolved  substance  cannot,  and  the  pure  solvent 
placed  upon  the  other  side,  the  pure  solvent  will  flow 
through  the  partition  into  the  solution.  This  phenomenon 
is  termed  osmosis,  and  the  pressure  thus  produced,  osmotic 
pressure.  We  may  demonstrate  this  phenomenon  by 
filling  a  bladder  with  a  solution  of  alcohol  in  water,  and 
then  immersing  it  in  pure  water.  Water  will  flow  through 
the  bladder  into  the  solution  of  alcohol,  and  the  bladder 
will  become  distended.  This  is,  of  course,  but  a  qualita- 
tive demonstration ;  and  were  we  dependent  upon  natural 
membranes  alone  to  measure  osmotic  pressure,  it  is  safe 
to  say  that  very  little  would  have  been  accomplished. 
Pfeffer,  however,  succeeded  in  devising  artificial  mem- 
branes, with  which  he  could  study  osmotic  pressure 
quantitatively. 

1  Osmotische  Untersuchungen,  Leipzig,  1877 ;  Harper's  Science  Series,  IV,  p.  3. 

71 


72  ELECTROLYTIC  DISSOCIATION 

Pfeffer's  Method  of  measuring  Osmotic  Pressure.  —  Cer- 
tain precipitates  have  the  property  of  allowing  the  solvent 
to  pass  through  them,  but  of  preventing  the  dissolved 
substance  from  passing.  If  these  precipitates  are  de- 
posited at  the  plane  of  contact  of  two  solutions,  or  of  a 
solution  and  a  solvent,  they  act  like  the  animal  mem- 
brane described  above.  This  important  fact  was  dis- 
covered by  Traube,  who  was  the  first  to  prepare  these 
artificial  membranes,  and  use  them  to  study  osmotic  press- 
ure. His  method,  however,  was  far  inferior  to  that 
devised  by  Pfeffer. 

To  make  these  membranes  more  resistant,  Pfeffer  de- 
termined to  form  them  upon  a  support.  He  states  that 
the  plant  cell  furnished  him  with  a  model.  "  In  these, 
the  plasma  membrane  which,  in  its  diosmotic  properties,  is 
similar  to  the  artificially  precipitated  membranes,  is  pressed 
against  the  cell  wall."  Pfeffer  caused  the  precipitate  to 
be  deposited  in  the  walls  of  very  fine-grained,  unglazed 
porcelain  cells.  The  precipitate  which  gave  him  the  best 
results  was  copper  ferrocyanide.  A  porcelain  cell  was 
filled  on  the  inside  with  a  solution  of  potassium  ferrocy- 
anide, and  immersed  in  a  solution  of  copper  sulphate. 
The  two  solutions  penetrated  the  walls  of  the  porcelain 
cell,  and  met  right  in  the  walls. 

Where  they  came  in  contact,  there  was  precipitated 
copper  ferrocyanide  as  a  membrane,  which,  when  the 
cell  was  broken,  appeared  as  a  fine  line. 

The  membranes  deposited  in  this  way  had  many  of 
the  properties  desired.  They  were  semipermeable,  i.e. 
allowed  the  solvent  to  pass  through  and  prevented  the 
dissolved  substance,  and  were  sufficiently  resistant  to 


THEORY  OF  ELECTROLYTIC   DISSOCIATION 


73 


withstand  considerable  pressure  without  breaking  The 
apparatus  in  its  complete  form,  as  used  by  Pfeffer,  is 
seen  in  Fig.  2. 

The  porcelain  cell,  with 
semipermeable  membrane 
deposited  in  the  walls,  is 
seen  at  z.  This  cell  was 
about  46  mm.  high,  16  mm. 
internal  diameter,  and  the 
walls  were  from  \\  to  2  mm. 
thick.  "The  narrow  glass 
tube  v,  called  the  connecting 
piece,  was  fastened  into  the 
porcelain  cell  with  fused 
sealing-wax,  and  the  closing 
piece  t  was  set  into  the  other 
end  of  this  tube  in  the  same 
manner.  The  shape  and 
purpose  of  this  are  shown 
in  the  figure.  The  glass  ring 
r  was  necessary  only  in 
experiments  at  higher  tem- 
perature, in  which  the  seal- 
ing-wax softened.  The  ring 
was  then  filled  with  pitch, 
which  also  held  together 
firmly  the  pieces  inserted 
into  one  another."  The 

From  "The  Modern  Theory  of  Solution." 

manometer    m    is    attached  Copyright-  18"'by  Harper&  Brothew- 

r  •          .ui.  FIG-  2' 

for  measuring  the  pressure. 

To  give  an  idea  of  the  precautions  which  are  necessary 


74  ELECTROLYTIC  DISSOCIATION 

to  prepare,  successfully,  such  semipermeable  membranes 
as  were  used  by  Pfeffer,  a  paragraph  is  quoted  from  his 
monograph  : 1  — 

"The  porcelain  cells  were  first  completely  injected  with 
water  under  the  air-pump,  and  then  placed  for  at  least 
some  hours  in  a  solution  containing  3  per  cent  of  copper 
sulphate,  and  the  interior  was  also  filled  with  this  solution. 
The  interior  only  of  the  porcelain  cell  was  then  once 
rinsed  out  quickly  with  water,  well  dried  as  rapidly  as 
possible  by  introducing  strips  of  filter  paper,  and  after 
the  outside  had  dried  off,  it  was  allowed  to  stand  some 
time  in  the  air  until  it  just  felt  moist.  Then  a  3  per 
cent  solution  of  potassium  ferrocyanide  was  poured  into 
the  cell,  and  this  immediately  reintroduced  into  the  solution 
of  copper  sulphate. 

"  After  the  cell  had  stood  undisturbed  for  from  twenty- 
four  to  forty-eight  hours,  it  was  completely  filled  with  the 
solution  of  potassium  ferrocyanide,  and  closed  as  shown 
in  Fig.  2.  A  certain  excess  of  pressure  of  the  contents 
of  the  cell  now  gradually  manifested  itself,  since  the  solu- 
tion of  potassium  ferrocyanide  had  a  greater  osmotic  press- 
ure than  the  solution  of  copper  sulphate.  After  another 
twenty-four  to  forty-eight  hours  the  apparatus  was  again 
opened,  and  generally  a  solution  introduced  which  con- 
tained 3  per  cent  of  potassium  ferrocyanide,  and  ij  per 
cent  of  potassium  nitrate  (by  weight),  and  which  showed 
an  excess  of  osmotic  pressure  of  somewhat  more  than  three 
atmospheres." 

The  osmotic  pressure  of  solutions  is  measured  with 
this  apparatus  as  follows :  The  cell  is  completely  filled 

1  Harper's  Science  Series,  IV,  p.  6. 


THEORY  OF   ELECTROLYTIC  DISSOCIATION 


7,5 


with  the  solution  and  then  tightly  closed.  The  solution 
also  extends  into  the  arm  of  the  manometer  attached 
to  the  cell.  The  whole  apparatus  is  then  immersed  in 
the  pure  solvent,  as 
shown  in  Fig.  3. 

The  closed  cell  is 
fastened  to  a  glass 
rod,  and  so  immersed 
in  the  liquid  in  the 
bath  that  the  entire 
manometer  is  covered. 
The  temperature  of 
the  bath  is  read  by 
thermometers.  The 
entire  apparatus  is 
placed  under  a  bell- 
jar  and  kept  in  a 
room  at  uniform  tem- 
perature. This  is 
necessary,  since  con- 
siderable time  is 
required  for  the  mer- 
cury to  reach  the 
highest  point  and 
remain  perfectly  sta- 
tionary. Water  flows 
in  through  the  semi- 
permeable  membrane, 
and  the  pressure  produced  is  finally  read  off  on  the  ma- 
nometer. The  water  which  enters  the  cell  dilutes  the  solu- 
tion and  diminishes  its  osmotic  pressure,  but  the  amount 


From  "  The  Modern  Theory  of  Solution." 
Copyright,  1899,  by  Harper  &  Brother*. 

FIG.  3. 


76  ELECTROLYTIC  DISSOCIATION 

of  water  which  enters  is  so  slight  that  the  error  from  this 
source  is  not  large. 

Some  of  Pfeffer's  Results.  —  Pfeffer  measured  the  os- 
motic pressure  of  solutions  of  a  number  of  substances  at 
different  concentrations,  and  at  different  temperatures.  A 
few  of  the  results  which  he  obtained  are  given. 

Osmotic  Pressure  for  Cane-Sugar  of  Different  Concentration 

PERCENTAGE  CONC.  BY  WEIGHT  OSMOTIC  PRESSURE 

i.o  535  mm. 

2.0  1016  mm. 

2.74  1518  mm. 

4.0  2082  mm. 

6.0  3°75 


Effect  of  Temperature  on  Osmotic  Pressure 

The  following  results  were  obtained  with  a  i  per  cent 
solution  of  cane-sugar  :  — 


TEMPERATURE  PRESSURE 

510  mm. 
544  mm. 


1 14.2°  C. 
1 32-0°  C. 


(  6.8°  C.  505  mm. 

|  13.7°  C.  525  mm. 

l22.o°C.  548mm. 

(I5-5°  C.  520  mm. 

36.0°  C.  567  mm. 

These  are  a  very  few  of  the  results  which  were  recorded 
by  Pfeffer. 

This  investigation  was  undertaken  by  Pfeffer  purely 
from  the  standpoint  of  vegetable  physiology,  and  with  no 


THEORY  OF  ELECTROLYTIC  DISSOCIATION  77 

idea  of  throwing  light  on  any  physical-chemical  problem. 
His  work  was  completed  and  published  irr  1877.  From 
the  botanical  standpoint  it  was  a  contribution  of  the  very 
highest  value.  Pfeffer  did  not  point  out  any  bearing 
which  his  results  might  have  on  problems  such  as  those 
with  which  we  are  now  about  to  deal.  Indeed,  their  sig- 
nificance was  not  seen  until  nearly  ten  years  later,  when 
van't  Hoff  showed  that  this  work  of  Pfeffer  marked  the 
beginning  of  a  new  era  in  physical  chemistry. 

RELATIONS  BETWEEN   OSMOTIC  PRESSURE  AND  GAS  PRESSURE 
DISCOVERED    BY    VAN*T    HOFF 

Historical.  —  In  following  up  the  discovery  of  a  great 
generalization,  it  is  always  of  interest  to  trace  the  stages 
by  which  it  was  reached.  We  are  very  fortunate  in  this 
case,  since  van't  Hoff  himself  has  given  us  an  account 
of  the  development  of  the  ideas  which  led  him  to  the 
discovery  of  the  relations  between  osmotic  pressure  and 
gas  pressure.  In  the  winter  of  1894,  he  was  invited  by 
the  German  Chemical  Society  to  give  a  lecture  on  his 
physical  chemical  investigations.  He  chose  for  his  theme, 
"  How  the  Theory  of  Solutions  Arose,"  and  here  we  find 
a  detailed  statement  of  the  steps  which  led  to  his  discov- 
ery. This  lecture  is  published  in  full  in  the  Berichte  der 
deutschen  chemischen  Gesellschaft,  27,  6  (1894).  A  few 
pages  from  this  lecture  are  given,  since  it  contains  a  con- 
cise statement  of  the  facts  which  are  of  such  unusual 
interest  in  this  connection. 

"  It  was  when  I  first  began  to  think  on  chemical  matters, 
under  the  guidance  of  Kekule  and  Wislicenus,  that  the  ideas 
about  the  position  of  atoms  in  space  began  to  germinate. 


78  ELECTROLYTIC  DISSOCIATION 

"  The  entire  '  Arrangement  of  Atoms  in  Space '  was,  in- 
deed, only  a  structure  which  depended  upon  the  relation 
of  a  physical  property  —  optical  activity  —  to  chemical 
constitution. 

"Although  so  young,  I  wished  then  to  know,  also,  the 
relations  between  constitution  and  chemical  properties. 
The  constitution  formula  should,  indeed,  be  the  expression 
of  the  entire  chemical  behavior. 

"Thus  arose  my  'Ansichten  iiber  die  organische  Chemie,' 
with  which,  indeed,  you  are  not  familiar,  and  which  is 
scarcely  worth  knowing.  It  had  this  value,  however,  for 
me,  that  it  pointed  out,  very  clearly,  the  existence  of  a  gap. 

"  Let  us  take  an  example  :  — 

"  It  is  known  that  oxygen  in  organic  compounds  has  an 
accelerating  action  on  almost  all  transformations.  The 
oxidation  of  CH4  is  more  difficult  than  of  CH3OH,  etc. 

"  To  obtain  relations  of  value  in  this  connection,  there  is 
need  of  accurate  knowledge  of  the  velocity  with  which  a 
reaction  proceeds,  and  thus  I  began  the  study  of  the 
velocity  of  reactions,  and  there  appeared  my  '  Etudes  de 
Dynamique  Chimique.' 

"  Reaction  velocity  was  at  first  the  chief  aim,  but  chemi- 
cal equilibrium  was  closely  associated  with  it.  Equilibrium 
resting,  on  the  one  hand,  on  the  equality  of  two  opposite 
reactions,  and  procuring  a  firm  support,  on  the  other, 
through  its  connection  with  thermodynamics.  You  see 
how,  to  obtain  my  object,  I  was  ever  led  farther  from 
it,  which  often  occurs. 

"And  I  must  go  still  farther ;  for  the  question  of  equilib- 
rium borders  directly  on  the  problem  of  affinity,  and  I  was 
thus  concerned  with  the  very  simple  affinity  phenomenon 


THEORY  OF  ELECTROLYTIC   DISSOCIATION  79 

—  at  first  with  that  which  expresses  itself  as  an  attraction 
for  water. 

"  Mitscherlich  had  already  raised  the  question,  in  his 
'Text-book  of  Chemistry'  (4th  edition,  1844,  565),  as  to 
the  magnitude  of  the  attractive  force  which  holds  the 
water  of  crystallization  in  Glauber  salts.  He  saw  a  means 
of  measuring  this  in  the  diminished  tension  of  the  water  of 
crystallization. 

" '  If  Glauber  salt  is  brought  into  the  barometric  vacuum 
at  9°,  the  mercury  falls  about  2\  lines  (5.45  mm.),  due  to 
the  liberation  of  water-vapor.  Water  itself  produces,  on 
the  other  hand,  a  fall  of  4  lines  (8.72  mm.).  The  affinity 
of  the  sodium  sulphate  for  its  water  of  crystallization  cor- 
responds, therefore,  to  the  difference,  i  \  lines  (3.27  mm.), 
i.e.  about  •£%  kg.  per  square  inch/ 

"  This  value,  % ^  of  an  atmosphere,  appeared  to  me  as 
small  without  precedent,  for  I  had  the  impression  that 
even  the  weakest  chemical  forces  are  very  large,  as 
appeared  to  me  to  follow  also  from  Helmholtz's  Faraday 
Lecture.  Thus,  the  question  arose,  whether  it  is  not  pos- 
sible, in  simpler  cases,  to  measure  this  attraction  for  water 
in  a  more  direct  way ;  and  for  this  purpose  the  aqueous 
solution  is  the  simplest  conceivable — much  simpler  than 
the  compound  containing  water  of  crystallization. 

"  Coming  from  the  laboratory  with  this  question  vividly  in 
mind,  I  met  my  colleague  De  Vries  and  his  wife.  He  was 
just  at  that  time  carrying  out  osmotic  investigations,  and 
he  told  me  about  Pfeffer's  determinations. 

"  You  recognize  the  apparatus  sketched  here.  The  so- 
called  osmotic  pressure  is  measured  with  a  battery  cell, 
whose  wall  is  made  semipermeable,  i.e.  permeable  only 


8o 


ELECTROLYTIC  DISSOCIATION 


to  water,  but  not  to  the  dissolved  substance,  e.g.  sugar  — . 
by  the  method  of  Traube.    This  is  accomplished  by  deposit- 


MITSCHERLICH 


PFEF 


ER 


FIG.  4. 


ing  a  membrane  of  copper  ferrocyanide  within  the  walls  of 
the  porcelain  cell.  The  osmotic  pressure  of  a  one  per  cent 
solution  of  cane-sugar  is  two-thirds  of  an  atmosphere. 

"This  pressure  was  remarkably  large  in  comparison  with 
that  described  by  Mitscherlich,  and  yet  a  relation  exists 
between  the  two. 

"  Let  us  consider  the  sugar  solution  as  placed  below,  on 
the  left  side,  and  separated  by  means  of  a  semipermeable 
membrane  from  water  which  is  on  the  right  side  below. 
The  movement  of  the  water  is  to  the  left,  into  the  space 
containing  vapor  with  the  pressure  observed  by  Mitscher- 
lich, into  the  water  with  that  observed  by  Pfeffer. 

"  A  calculation  can  be  based  directly  upon  this  relation. 
The  force  described  by  Mitscherlich  is  very  small,  because 
it  acts  on  the  more  dilute  vapor ;  that  of  Pfeffer  is  large, 
because  it  acts  on  the  concentrated  water.  Therefore :  — 


THEORY  OF   ELECTROLYTIC  DISSOCIATION  8 1 

Pfeffer  :  Mitscherlich  =  1000  :  —0.08956— (i  +  — /), 

760  2  273  ' 

and  thus  Pfeffer's  force,  calculated  from  the  decrease  in 
tension  (freezing-point) :  — 

TEMPERATURE  OSMOTIC  PRESSURE  0.00239  T 

6.8°  0.664  0-668 

15.5°  0.684  0-689 

22°  0.721  0.704 

32°  0.716  0.728 

36°  0.746  0.737 

The  above  proportionality  is,  however,  not  perfectly 
rigid.  The  exact  formula  is  obtained,  in  case  the  work 
which  the  water  attraction  can  perform  is  chosen  as  the 
starting-point.  This  is  independent  of  whether  the  water 
is  carried  over  as  such,  or  as  vapor ;  and  thus  we  have  the 
relation  (for  1 8  kgs.  water) :  — 

—PV, 
Pi      323 

in  which  pw  and  pl  are,  respectively,  the  tension  of  the 
water  and  of  the  solution,  P  the  osmotic  pressure  in  kgs. 
per  qm.,  and  Fthe  volume  of  18  kgs.  of  water  in  cbm. 

"  This  formula  corresponds  very  accurately  with  Pfeffer's 
results,  but  it  can  be  used  for  determining  pressure  only 
in  case  the  tension  pl  is  known ;  and  thus  Mitscherlich 's 
question  of  water  of  crystallization  is  also  solved,  since 
it  is  evident  that  this  water  attraction  corresponds  to  that 
of  a  solution  of  equal  maximum  tension.  We  have  then 
the  following :  — 


82  ELECTROLYTIC  DISSOCIATION 

SUBSTANCE  TEMPERATURE  PRESSURE 

Na2SO4. 10  H2O  9°  600  atmos. 

FeSO4.    7  H2O  25°  510  atmos. 

FeSO4 .    7  H2O  65°  245  atmos. 

CuSO4.   5  H2O  50°  nooatmos. 

CuSO4.   3  H2O  1 730  atmos. 

"  This  means  that  if  Na2SO4  should  be  prevented  from 
taking  up  its  water  by  pressure,  in  a  suitable  manner,  — 
say  in  Pfeffer's  apparatus,  —  600  atmospheres  at  9°  would 
be  necessary  and  sufficient 

"We  must  now  turn  from  Mitscherlich's  question  of  affin- 
ity to  dilute  solutions ;  since  where  we  are  dealing  with  the 
union  of  water  of  crystallization,  it  is  obvious  that  enor- 
mous concentrations  obtain." 

We  see  from  the  above  paragraphs,  the  exact  stages  by 
which  van't  Hoff  arrived  at  the  study  of  dilute  solutions 
from  the  standpoint  of  osmotic  pressure.  From  the  posi- 
tion of  atoms  in  space,  he  was  led  to  study  reaction  velocity, 
and  from  this  the  conditions  of  equilibrium.  But  closely 
connected  with  the  problem  of  equilibrium  was  that  of 
affinity.  He  took  up,  as  an  example  of  affinity,  the  attrac- 
tion of  salts  for  their  water  of  crystallization,  and  sought 
to  measure  this  more  directly  than  had  been  done.  This 
led  him,  through  the  suggestion  of  De  Vries,  directly  to 
Pfeffer's  osmotic  investigations.  Having  dealt  with  con- 
centrated solutions,  he  then  turned  to  dilute ;  and  we  shall 
now  learn  the  nature  of  the  results  which  he  obtained,  by 
comparing  the  gas  pressure  of  gases  with  the  osmotic 
pressure  of  dilute  solutions. 

Boyle's  Law  for  Dilute  Solutions. — In  1887  van't  Hoff 
published  a  paper  in  the  first  volume  of  the  Zeitschrift 


THEORY   OF   ELECTROLYTIC   DISSOCIATION  83 

fur  physikaliscJie  CJiemie,  under  the  title,  "The  R61e  of 
Osmotic  Pressure  in  the  Analogy  between  Solutions  and 
Gases."  !  The  object  of  this  communication,  as  its  title  im- 
plies, is  to  point  out  certain  relations  between  the  gas  press- 
ure of  gases  and  the  osmotic  pressure  of  dilute  solutions.  To 
quote  from  the  translation  in  Harper's  Science  Series :  — 

"  The  analogy  between  dilute  solutions  and  gases  acquires 
at  once  a  more  quantitative  form,  if  we  consider  that  in 
both  cases  the  change  in  concentration  exerts  a  similar 
influence  on  the  pressure ;  and,  indeed,  the  values  in  ques- 
tion are,  in  both  cases,  proportional  to  one  another. 

"  This  proportionality,  which,  for  gases,  is  designated  as 
Boyle's  law,  can  be  shown  for  osmotic  pressure,  experi- 
mentally from  data  already  at  hand,  and  also  theoretically." 

Van't  Hoff  then  gives  enough  of  Pfeffer's  data  to  show 
experimentally,  that  there  is  proportionality  between  os- 
motic pressure  and  concentration. 

"  Let  us  first  give  the  results  of  Pfeffer's  determinations 
of  osmotic  pressure  (P),  in  solutions  of  sugar,  at  the  same 
temperature  (13.2°  to  16.1°)  and  different  concentrations 

(C):-          c  f  L 

Cx 

i%  535  mm-  535 

2%  1016  mm.  508 

2.74%  1518  mm.  554 

4%  2082  mm.  521 

6%  3075  mm.  513 

p 

"  The  nearly  constant  value  of  —  indicates  that,  in  fact,  a 

C"- 

proportionality  between  pressure  and  concentration  exists."2 

1  Ztschr.  phys.  Chem.,  i,  481.    Translated  into  English  by  H.  C.  Jones.    Har- 
per's Science  Series,  IV,  p.  13. 

2  Harper's  Science  Series,  IV,  p.  16. 


84  ELECTROLYTIC   DISSOCIATION 

The  work  of  De  Vries1  is  then  cited,  as  furnishing  a 
second  line  of  experimental  evidence,  of  the  applicability  of 
Boyle's  law  to  the  osmotic  pressure  of  dilute  solution.  De 
Vries  compared  the  osmotic  pressure  of  solutions  of  sugar, 
potassium  nitrate,  and  potassium  sulphate,  with  that  of  the 
contents  of  a  plant  cell,  whose  protoplasmic  sac  contracts 
when  the  cell  is  introduced  into  a  solution  which  has 
stronger  attraction  for  water.  It  was  found  that  equal 
changes  in  concentration  of  solutions  of  sugar,  potassium 
nitrate,  and  potassium  sulphate,  exert  the  same  influence 
on  the  osmotic  pressure.  The  experimental  evidence  was 
thus  very  strongly  in  favor  of  the  law  of  Boyle  for  the 
osmotic  pressure  of  solutions. 

A  theoretical  demonstration  of  this  law  for  solutions  was 
also  given  by  van't  Hoff  :2  — 

Gay  Lussac's  Law  for  Dilute  Solutions.  —  Having  found 
that  the  law  of  Boyle  for  gases  applies  to  the  osmotic 
pressure  of  solutions,  one  would  naturally  inquire  whether 
other  gas  laws  also  apply  to  solutions.  Thus,  the  attempt 
was  made  to  apply  to  the  osmotic  pressure  of  solutions 
the  law  of  Gay  Lussac,  which  holds  for  the  tempera- 
ture coefficient  of  gas  pressure.  The  law  was  tested 
both  experimentally  and  theoretically  on  thermodynariiic 
grounds. 

For  experimental  demonstration,  recourse  was  had  again 
to  the  results  of  Pfeffer's  investigations.  This  investiga- 
tor found  that  the  osmotic  pressure  always  increased  with 
rise  in  temperature.  If  from  one  of  two  experiments 
carried  out  with  the  same  solution  at  different  tempera- 

1  "  Eine  Methode  zur  Analyse  der  Turgorkraft,"  Pringsheim's  Jahrb.,14. 

2  See  Harper's  Science  Series,  IV,  17. 


THEORY  OF   ELECTROLYTIC  DISSOCIATION  85 

tures  we  calculate  the  result  of  the  other,  on  the  assump- 
tion of  Gay  Lussac's  law,  and  compare  it  with  the  value 
directly  obtained,  we  have  the  following  relations :  — 

1.  Solution  of  cane-sugar.1 

At  32°  a  pressure  of  544  mm.  was  observed. 
At  14.15°  the  calculated  pressure  is  512  mm.,  instead  of 
510  as  found  by  experiment. 

2.  Solution  of  cane-sugar. 

At  36°  the  pressure  observed  was  567  mm. 
At  15.5°  the  calculated  pressure  is  529  mm.,  instead  of 
520.5  mm.  as  found  experimentally. 

3.  Solution  of  sodium  tartrate. 

At  37.3°  the  pressure  observed  was  983  mm. 

At  13.3°  the  calculated  pressure  is  907  mm.,  instead  of 
908  found  by  experiment. 

There  is  evidently  a  close  approximation,  in  the  above 
results,  between  the  observed  and  calculated  values. 

The  law  of  Gay  Lussac,  as  applied  to  the  osmotic  press- 
ure of  solutions,  received  further  experimental  support 
from  the  work  of  Bonders  and  Hamburger.2  They 
worked  with  animal  cells  (blood  corpuscles)  in  a  manner 
similar  to  De  Vries.  They  found  that  solutions  of  potas- 
sium nitrate,  sodium  chloride,  and  sugar,  which  have  the 
same  osmotic  pressure  as  the  contents  of  the  cells  in  ques- 
tion, at  o°,  and  therefore  the  same  as  one  another,  show 
exactly  the  same  relation  at  34°,  i.e.  all  have  the  same 
osmotic  pressure  at  this  higher  temperature. 

This  shows  that  the  temperature  coefficient  of  osmotic 

1  Harper's  Science  Series,  IV,  p.  19. 

2  Onderzoekingen  gedaan  in  het  physiologisth,  Laboratorium  der  Utrechtsche 
lloogeschool  [3],  9,  26. 


86  ELECTROLYTIC  DISSOCIATION 

pressure  for  solutions  of  these  three  substances  is  the 
same;  and,  taken  with  Pfeffer's  results,  is  strong  evi- 
dence in  favor  of  the  law  of  Gay  Lussac  as  applied  to 
solutions. 

Experimental  Evidence  in  Favor  of  both  the  Laws  of 
Boyle  and  Gay  Lussac  for  Solutions.  —  It  was  observed  by 
Soret,1  that  if  a  homogeneous  solution  is  placed  in  a  tube, 
and  the  top  of  the  tube  kept  warmer  than  the  bottom, 
the  solution  will  not  remain  homogeneous,  but  will  become 
more  concentrated  in  the  colder  portion.  This  is  exactly 
analogous  to  what  would  occur  with  a  gas ;  the  colder 
portion  would  become  more  concentrated.  The  experi- 
ments were  made  by  Soret  in  vertical  tubes,  the  upper 
portions  of  which  were  warmed  to  a  constant  temperature, 
and  the  lower  portions  cooled  to  a  constant  temperature. 
It  was  soon  found,  as  would  be  expected,  that  the  time 
required  to  establish  equilibrium  was  much  greater  for 
solutions  than  for  gases. 

How  does  the  "  Principle  of  Soret "  throw  any  light  on 
the  applicability  of  the  laws  of  Boyle  and  Gay  Lussac  to 
solutions  ?  A  gas  will  always  distribute  itself  in  a  space 
so  that  the  gas  pressure  is  the  same  at  every  point  in  the 
space.  If  one  portion  of  the  space  is  colder  than  another, 
the  gas  pressure  of  any  given  molecule  in  this  portion 
will  be  less  than  in  the  warmer  portion ;  therefore,  more 
gas  particles  must  collect  in  the  colder  portion,  to  give  the 
same  pressure  as  in  the  warmer  portion  of  the  tube. 

Similarly,  with  solutions,  the  dissolved  substance  will 
distribute  itself  throughout  the  solvent,  so  that  the  osmotic 
pressure  is  the  same  at  every  point  in  the  solution.  If 

1  Archives  des  Sciences  Phys.  et  Nat.  [3],  2,  48;  Ann.  Chim.  Phys.  [5],  22,  293. 


THEORY  OF  ELECTROLYTIC  DISSOCIATION  87 

one  part  of  the  solution  is  colder  than  another,  a  dissolved 
particle  will  exert  less  osmotic  pressure  where  the  solution 
is  colder.  It  will,  therefore,  require  more  particles  in  the 
colder  region,  to  exert  a  given  pressure,  than  in  the  warmer 
region.  We  can  calculate  the  change  in  concentration  of 
a  gas  with  change  in  temperature,  from  the  laws  of  Boyle 
and  Gay  Lussac.  Similarly,  if  the  laws  of  Boyle  and  Gay 
Lussac  apply  to  the  osmotic  pressure  of  solutions,  we  can 
calculate  the  difference  in  concentrations  between  the 
colder  and  warmer  parts  of  a  solution,  for  a  given  differ- 
ence in  the  temperature  of  these  two  regions.  Then,  the 
difference  in  the  concentrations  of  the  two  parts  can  be 
determined  experimentally,  and  the  calculated  results  com- 
pared with  the  results  of  experiment. 

This  has  been  done  for  solutions  of  copper  sulphate, 
and  the  following  results  are  given  by  van't  Hoff :  — 

1.  Solution  of  copper  sulphate. 

The  part  cooled  to  20°  contained  17.332  per  cent.  The 
concentration  calculated  for  80°,  is  14.3  per  cent.  That 
found  experimentally  was  14.03  per  cent. 

2.  Solution  of  copper  sulphate. 

The  part  cooled  to  20°  contained  29.867  per  cent.  24.8 
per  cent  was  calculated  for  80°,  while  23.871  per  cent  was 
found. 

It  should  be  observed,  that  the  results  found  by  experi- 
ment are  slightly  lower  than  those  calculated  on  the  basis 
of  the  laws  of  Boyle  and  Gay  Lussac,  yet  the  difference  is 
only  slight.  It  must,  however,  be  stated  in  this  connection, 
that  it  has  been  shown  that  the  time  required  to  establish 
equilibrium  in  a  solution  is  much  greater  than  was  formerly 
supposed,  and  in  the  earlier  experiments  not  enough  time 


88  ELECTROLYTIC  DISSOCIATION 

was  allowed  for  the  final  equilibrium  to  be  reached.  Con- 
sequently, the  difference  in  concentration  between  the 
colder  and  the  warmer  portions  of  the  tube,  as  found  by 
experiment,  was  less  than  the  calculated,  since  the  latter 
was  based  on  perfect  equilibrium  having  been  reached. 
More  recent  experiments,  in  which  the  tubes  have  been 
allowed  to  stand  for  several  months,  give  results  which 
agree  very  closely  with  the  calculated,  and  thus  the  "  Prin- 
ciple of  Soret"  is  a  strong  experimental  support,  to  the 
applicability  of  the  laws  of  Boyle  and  Gay  Lussac  to  the 
osmotic  pressure  of  dilute  solutions. 

Avogadro's  Law  for  Dilute  Solutions.  —  It  has  been 
shown,  thus  far,  that  the  osmotic  pressure  of  solutions  is 
proportional  to  the  concentration,  and,  also,  that  the  tem- 
perature coefficient  of  osmotic  pressure  is  the  same  as  that 
of  gas  pressure.  In  a  word,  gas  pressure  and  osmotic 
pressure  are  analogous,  both  obeying  the  laws  of  Boyle 
and  Gay  Lussac. 

The  more  important  question,  however,  still  remains : 
What  is  the  relation  between  the  actual  osmotic  pressure 
exerted  by  a  dissolved  particle,  and  the  gas  pressure  of  a 
gaseous  particle,  under  the  same  conditions  of  temperature 
and  concentration  ?  Van't  Hoff  answered  this  question 
both  experimentally  and  theoretically. 

He  found  in  Pfeffer's  determinations  of  the  osmotic 
pressure  of  cane-sugar,  an  experimental  solution  of  this 
problem.  The  osmotic  pressure  of  a  sugar  solution  of 
known  concentration  was  compared  with  the  gas  pressure 
of  hydrogen  gas,  containing  the  same  number  of  particles 
in  a  given  space.  A  i  per  cent  solution  of  sugar  was 
used.  Hydrogen  of  the  same  concentration  would  con- 


THEORY   OF   ELECTROLYTIC  DISSOCIATION  89 

tain  3^2  x  10  grams  per  litre,  i.e.  0.0581  gram  per  litre. 
Since  hydrogen  at  o°  and  atmospheric  pressure  weighs 
0.08956  gram  per  litre,  hydrogen  under  the  above  condi- 
tions would  exert  a  pressure  of  -^ atmosphere  at  o°. 

0.08956 

or  0.649  atmosphere;  and  at  t°  of  0.649(1  +  0.00367 /) 
atmosphere. 

Comparing  this  at  different  temperatures  with  Pfeffer's 
results,  we  have :  — 

TEMPERATURE  OSMOTIC  PRESSURE  GAS  PRESSURE 

6.649(1  -i-  0.00367 1) 

6.8  0.664  0.665 

13.7  0.691  0.681 

14.2  0.671  0.682 

15.5  0.684  0.686 

22.0  0.721  0.701 

32.0  0.716  °-725 

36.0  0.746  0.735 

These  results  suffice  to  bring  out  the  relation,  that  the 
osmotic  pressure  of  a  solution  of  sugar  at  a  given  tem- 
perature is  exactly  eqiial  to  the  gas  pressure  of  a  gas,  which 
contains  the  same  number  of  molecules  in  a  given  volume 
as  there  are  sugar  molecules  in  the  same  volume  of  the 
sohition. 

This  relation  has  been  found  to  hold  for  such  a  large 
number  of  substances,  that  we  are  led  to  the  all-important 
generalization  :  that  the  osmotic  pressure  of  a  dissolved 
particle  is  exactly  equal  to  the  gas  pressure  of  a  gaseous 
particle  at  the  same  temperature  and  concentration. 

The  law  of  Avogadro,  applied  to  gases,  states  that  equal 
volumes  of  all  gases,  at  the  same  temperature  and  pressure, 
contain  the  same  number  of  ultimate  particles. 


90  ELECTROLYTIC  DISSOCIATION 

The  law  of  Avogadro,  as  applied  to  solutions,  states  that 
solutions  which,  at  the  same  temperature,  have  the  same 
osmotic  pressure,  contain  in  a  given  volume  the  same  num- 
ber of  dissolved  particles. 

Van't  Hoff  has  shown  that  the  law  of  Avogadro,  as 
applied  to  solutions,  is  confirmed  also  by  the  lowering  of 
the  vapor-tension,  and  of  the  freezing-point  of  the  solvent, 
produced  by  the  dissolved  substance. 

He  has  also  given  a  thermodynamic  demonstration  of 
the  law.1 

General  Expression  of  the  Laws  of  Boyle,  Gay  Lussac, 
and  Avogadro,  for  Solutions  and  Gases.  —  Having  shown 
that  the  three  laws  of  gas  pressure  apply  to  the  osmotic 
pressure  of  solutions,  van't  Hoff  attempted  to  furnish  a 
general  expression  for  these  three  laws.  "The  well- 
known  formula,  which  expresses  for  gases  the  two  laws  of 
Boyle  and  Gay  Lussac :  — 

PV=RT, 

is  now,  where  the  laws  referred  to  are  also  applicable  to 
liquids,  valid  also  for  solutions,  if  we  are  dealing  with  the 
osmotic  pressure.  This  holds  even  with  the  same  limita- 
tion, which  is  also  to  be  considered  with  gases,  that  the 
dilution  shall  be  sufficiently  great  to  allow  one  to  disre- 
gard the  reciprocal  action  of,  and  the  space  taken  by,  the 
dissolved  particles. 

"If  we  wish  to  include  in  the  above  expression  also  the 
third,  the  law  of  Avogadro,  this  can  be  done  in  an  exceed- 
ingly simple  manner,  following  the  suggestion  of  Horst- 
mann,2  considering  always  kilogram  molecules  of  the 

1  See  Harper's  Science  Series,  IV,  22.  2  Ber.  d.  chem.  Gesell.,  14,  1243. 


THEORY   OF   ELECTROLYTIC  DISSOCIATION  91 

substance  in  question;  thus,  2  k.  hydrogen,  44  k.  carbon 
dioxide,  etc.  Then  R  in  the  above  equation  has  the  same 
value  for  all  gases,  since,  at  the  same  temperature  and 
pressure,  the  quantities  mentioned  occupy  also  the  same 
volume.  If  this  value  is  calculated,  and  the  volume  taken 
in  Mr3,  the  pressure  in  K°  per  Mr2,  and  if,  for  example, 
hydrogen  at  o°  and  atmospheric  pressure  is  chosen  :  — 

=  845.05-     .: 


The   combined   expression   of   the    laws    of    Boyle,   Gay 
Lussac,  and  Avogadro  is  then  :  — 


and,  in  this  form,  it  refers  not  only  to  gases,  but  to  all  solu- 
tions, P  being  then  always  taken  as  osmotic  pressure."  l 
The  conclusion  from  what  has  thus  far  been  given  of 
van't  Hoff's  paper  is  that  the  three  laws  of  gas  pressure 
apply  directly  to  the  osmotic  pressure  of  solutions,  and 
this  is  perfectly  general  for  solutions  such  as  we  have  been 
considering.  But  there  are  many  exceptions,  and  these 
are  of  even  more  interest  than  the  cases  which  conform  to 
the  laws  of  gas  pressure. 

Exceptions  to  the  General  Applicability  of  the  Gas  Laws 
to  Osmotic  Pressure.  —  While  the  osmotic  pressures  of 
solutions  of  compounds  like  cane-sugar  conform  to  the 
gas  laws,  the  osmotic  pressures  of  large  classes  of  chemical 
substances  do  not  conform  to  these  laws.  The  excep- 
tions include  all  the  acids,  all  the  bases,  and  all  the  salts. 
If  we  will  consider  the  number  of  compounds  contained  in 

1  Harper's  Science  Series,  IV,  24. 


92  ELECTROLYTIC   DISSOCIATION 

these  three  classes,  it  is  a  question  whether  the  exceptions 
will  not  outnumber  the  cases  which  conform  to  rule. 

All  of  these  compounds  give  an  osmotic  pressure,  which 
is  greater  than  would  be  expected  from  the  gas  laws. 

The  expression  PV=RT  no  longer  applies  to  the 
osmotic  pressure  of  these  substances,  and,  therefore,  a 
coefficient  was  introduced  by  van't  Hoff ;  when  the  expres- 
sion became :  — 

PV=iRT. 

This  coefficient,  which  for  acids,  bases,  and  salts  is  always 
greater  than  unity,  has  come  to  be  known  as  the  "van't 
Hoff  i"  What  was  the  real  physical  or  chemical  signifi- 
cance of  these  exceptions  ?  Why  does  a  large  class  of 
compounds  show  an  osmotic  pressure  which  conforms  to 
the  gas  laws,  and  yet  a  very  large  class  give  an  osmotic 
pressure  which  is  always  too  great  ? 

Van't  Hoff  saw  clearly  the  discrepancy  which  existed 
here,  as  will  be  seen  from  his  own  words :  "  If  we  are  still 
considering  '  ideal  solutions/  a  class  of  phenomena  must  be 
dealt  with  which,  from  the  now  clearly  demonstrated 
analogy  between  solutions  and  gases,  are  to  be  classed 
with  the  earlier  so-called  deviations  from  Avogadro's  law. 
As  the  pressure  of  the  vapor  of  ammonium  chloride,  for 
example,  was  too  great  in  terms  of  this  law,  so,  also,  in  a 
large  number  of  cases,  the  osmotic  pressure  is  abnormally 
large,  and  in  the  first  case,  as  was  afterwards  shown,  there 
is  a  breaking  down  into  hydrochloric  acid  and  ammonia,  so, 
also,  with  solutions,  we  would  naturally  conjecture  that,  in 
such  cases,  a  similar  decomposition  had  taken  place.  Yet 
it  must  be  conceded  that  anomalies  of  this  kind,  existing 


THEORY   OF   ELECTROLYTIC  DISSOCIATION  93 

in  solutions,  are  much  more  numerous,  and  appear  with 
substances  which  it  is  difficult  to  assume  break  down  in 
the  usual  way.  Examples  in  aqueous  solutions  are  most  of 
the  salts,  the  strong  acids,  and  the  strong  bases.  ...  It 
may  then  have  appeared  daring  to  give  Avogadro's  law 
for  solutions  such  a  prominent  place,  and  I  should  not 
have  done  so,  had  not  Arrhenius  pointed  out  to  me,  by 
letter,  the  probability  that  salts  and  analogous  substances, 
when  in  solution,  break  down  into  ions."  1 

The  last  sentence  gives  us  the  connecting  link  between 
the  generalization  reached  by  van't  Hoff,  and  the  discovery 
of  the  theory  of  electrolytic  dissociation.  The  latter  we 
owe  to  the  Swedish  physicist,  Arrhenius,  to  whose  work  we 
will  now  turn. 

ON  THE   DISSOCIATION  OF  SUBSTANCES  DISSOLVED  IN  WATER 
BY    SVANTE   ARRHENIUS 

A  paper,2  under  the  above  title,  appeared  in  the  same 
volume  of  the  Zeitschrift  fur  physikalische  Chemie,  as  the 
paper  by  van't  Hoff  which  we  have  just  considered. 
Arrhenius  was  impressed  by  the  generalizations  reached 
by  van't  Hoff,  and  especially  by  the  large  number  of 
exceptions.  This  will  be  seen  best  by  quoting  the  words 
with  which  Arrhenius  began  his  paper. 

"  In  a  paper  submitted  to  the  Swedish  Academy  of 
Sciences,  on  the  I4th  of  October,  1885,  van't  Hoff  proved 
experimentally,  as  well  as  theoretically,  the  following  un- 
usually significant  generalization  of  Avogadro's  law :  — 

1  Harper's  Science  Series,  IV,  34. 

2  Ztschr.  phys.  Chem.,  i,  631  (1887).    Translated  into  English  by  H.  C.  Jones. 
Harper's  Science  Series,  IV,  47. 


94  ELECTROLYTIC  DISSOCIATION 

"The  pressure  which  a  gas  exerts  at  a  given  temperature, 
if  a  definite  number  of  molecules  is  contained  in  a  definite 
volume,  is  equal  to  the  osmotic  pressure  which  is  produced 
by  most  substances  under  the  same  conditions,  if  they  are 
dissolved  in  any  given  liquid."  1 

"Van't  Hoff  has  proved  this  law  in  a  manner  which 
scarcely  leaves  any  doubt  as  to  its  absolute  correctness. 
But  a  difficulty  which  still  remain's  to  be  overcome,  is  that 
the  law  in  question  holds  only  for  'most  substances,'  a 
very  considerable  number  of  the  aqueous  solutions  investi- 
gated furnishing  exceptions ;  and  in  the  sense  that  they 
exert  a  much  greater  osmotic  pressure  than  would  be 
required  from  the  law  referred  to." 

The  above  are  the  words  with  which  Arrhenius  stated 
the  problem ;  we  will  now  follow  the  line  of  thought  which 
led  him  to  its  solution. 

"  If  a  gas  shows  such  a  deviation  from  the  law  of  Avo- 
gadro,  it  is  explained  by  assuming  that  the  gas  is  in  a  state 
of  dissociation.  The  conduct  of  chlorine,  bromine,  and 
iodine,  at  higher  temperatures,  is  a  very  well-known 
example.  We  regard  these  substances,  under  such  con- 
ditions, as  broken  down  into  simple  atoms. 

"The  same  expedient  may,  of  course,  be  made  use  of  to 
explain  the  exceptions  to  van't  HofFs  law;  but  it  has  not 
been  put  forward  up  to  the  present,  probably  on  account 
of  the  newness  of  the  subject,  the  many  exceptions  known, 
and  the  vigorous  objections  which  would  be  raised  from 
the  chemical  side  to  such  an  explanation.  The  purpose 
of  the  following  lines  is  to  show  that  such  an  assumption, 

1  Van't  Hoff,  Une  propri6t6  g6n6rale  de  la  matiere  dilute,  p.  43.  Sv.  Vet-ak-s 
Handlingar,  21,  Nr.  17,  1886. 


THEORY   OF   ELECTROLYTIC  DISSOCIATION  95 

of  the  dissociation  of  certain  substances  dissolved  in  water, 
is  strongly  supported  by  the  conclusions  drawn  from  the 
electrical  properties  of  the  same  substances,  and  that,  also, 
the  objections  to  it  from  the  chemical  side  are  diminished 
on  more  careful  examination."  1 

Arrhenius  then  offers  his  explanation  of  the  exceptions 
to  van't  Hoff's  generalization.  As  we  shall  see,  he  goes 
back  to  the  theory  put  forward  by  Clausius  to  account  for 
electrolysis,  and  which  has  already  been  considered,  in  con- 
nection with  the  development  of  electrochemistry  (p.  48). 

"In  order  to  explain  the  electrical  phenomena,  we  must 
assume  with  Clausius,2  that  some  of  the  molecules  of  an 
electrolyte  are  dissociated  into  their  ions,  which  move  inde- 
pendent of  one  another.  But  since  the  '  osmotic  pressure ' 
which  a  substance  dissolved  in  a  liquid  exerts  against  the 
walls  of  the  confining  vessel  must  be  regarded,  in  accord- 
ance with  the  modern  kinetic  view,  as  produced  by  the 
impacts-  of  the  smallest  parts  of  this  substance,  as  they 
move  against  the  walls  of  the  vessel,  we  must  therefore 
assume,  in  accordance  with  this  view,  that  a  molecule  dis- 
sociated in  the  manner  given  above,  exercises  as  great  a 
pressure  against  the  walls  of  the  vessel  as  its  ions  would  do 
in  the  free  condition.  If,  then,  we  could  calculate  what 
fraction  of  the  molecules  of  an  electrolyte  is  dissociated 
into  ions,  we  should  be  able  to  calculate  the  osmotic  press- 
ure from  van't  Hoff's  law."  3 

We  see  from  the  above,  that  the  simple  qualitative  sug- 
gestion, that  some  molecules  are  broken  down  into  parts  or 

1  Harper's  Science  Series,  IV,  48. 

2  Pogg.  Ann.,  101,  347 ;  Wied.  Elektr.,  2,  941.  ' 

3  Harper's  Science  Series,  IV,  48. 


96  ELECTROLYTIC   DISSOCIATION 

ions,  is  not  new  with  Arrhenius.  This  theory,  as  already 
stated,  had  been  advanced  some  thirty  years  before  by 
Clausius.  The  new  feature,  which  was  introduced  by 
Arrhenius,  was  to  point  out  a  method  of  determining  just 
what  per  cent  of  the  molecules  are  broken  down  into  ions. 
The  merely  qualitative  suggestion  of  Clausius  was  thus 
converted  into  a  definite  theory,  which  could  be  tested 
experimentally.  The  method  of  calculating  the  amount  of 
dissociation  into  ions,  as  worked  out  by  Arrhenius,  will 
now  be  given  in  his  own  words. 

"In  a  former  communication,  'On  the  Electrical  Con- 
ductivity of  Electrolytes,'  I  have  designated  those  mole- 
cules, whose  ions  are  independent  of  one  another  in  their 
movements,  as  active;  the  remaining  molecules,  whose  ions 
are  firmly  combined  with  one  another,  as  inactive.  I  have 
also  maintained  it  as  probable,  that  in  extreme  dilution,  all 
the  inactive  molecules  of  an  electrolyte  are  transformed 
into  active.1  This  assumption  I  will  make  the  basis  of  the 
calculations  now  to  be  carried  out.  I  have  designated  the 
relation  between  the  number  of  active  molecules,  and  the 
sum  of  the  active  and  inactive  molecules,  as  the  activity 
coefficient.2  The  activity  coefficient  of  an  electrolyte  at 
infinite  dilution  is  therefore  taken  as  unity.  For  smaller 
dilution  it  is  less  than  one,  and  from  the  principles  estab- 
lished in  my  work  already  cited,  it  can  be  regarded  as  equal 
to  the  ratio  of  the  actual  molecular  conductivity  of  the 
solution,  to  the  maximum  limiting  value  which  the  mo- 
lecular conductivity  of  the  same  solution  approaches  with 


1  Bihang  der  Stockholmer  Akademie,  8,  Mr.  13  and  14,  2  Tl.,  pp.  5  and  13  ; 
i  Tl.,  p.  6. 

2  Loc.  cit.,  2  Tl.,  p.  5. 


THEORY  OF  ELECTROLYTIC  DISSOCIATION  97 

increasing  dilution.  This  obtains  for  solutions  which  are 
not  too  concentrated  (i.e.  for  solutions  in  which  disturbing 
conditions,  such  as  internal  friction,  etc.,  can  be  disre- 
garded). If  this  activity  coefficient  (a)  is  known,  we  can 
calculate,  as  follows,  the  values  of  the  coefficient  z,  tabu- 
lated by  van't  Hoff :  i  is  the  relation  between  the  osmotic 
pressure  actually  exerted  by  a  substance,  and  the  osmotic 
pressure  which  it  would  exert,  if  it  consisted  only  of  inac- 
tive (undissociated)  molecules,  i  is  evidently  equal  to  the 
sum  of  the  number  of  inactive  molecules,  plus  the  number 
of  ions,  divided  by  the  sum  of  the  inactive  and  active 
molecules.  If,  then,  m  represents  the  number  of  inactive, 
and  n  the  number  of  active,  molecules,  and  k  the  number 
of  ions  into  which  every  active  molecule  dissociates  (e.g., 
k  =  2  for  KC1,  i.e.K  and  Cl;  k  =  3  for  BaCl2  and  K2SO4, 
i.e.  Ba,  Cl,  Cl,  and  K,  K,  SO4),  then  we  have :  — 

.  __  m  +  kn 
m  -f-  n 

"  But  since  the  activity  coefficient  (a)  can,  evidently,  be 
n 


written 


m  -f-  n 


Arrhenius  thus  shows  how  it  is  possible  to  calculate  the 
value  of  the  van't  Hoff  coefficient  i,  knowing  the  activity 
coefficient  («),  which  can  be  determined  directly  from  the 
conductivity  of  the  solution. 

He  then  shows  how  the  value  of  i  can  be  calculated  also 
from  the  lowering  of  the  freezing-point  of  water  produced 
by  the  dissolved  substance. 

l  Harper's  Science  Series,  IV,  48, 


98  ELECTROLYTIC  DISSOCIATION 

"  On  the  other  hand,  i  can  be  calculated  as  follows,  from 
the  results  of  Raoult's  experiments  on  the  freezing-point 
of  solutions,  making  use  of  the  principles  stated  by  van't 
Hoff.  The  lowering  (i)  of  the  freezing-point  of  water  (in 
degrees  Celsius),  produced  by  dissolving  a  gram-mole- 
cule of  the  given  substance  in  one  litre  of  water,  is  divided 

by  18.5:-  t   „! 

18.5' 

Arrhenius  then  compared  the  values  of  i,  calculated 
from  the  conductivity  of  solution,  with  the  values  calcu- 
lated from  the  freezing-point  lowerings,  to  see  whether  the 
two  series  would  agree  with  one  another.  He  made  the 
comparison  for  a  large  number  of  bases,  acids,  and  salts, 
and  also  for  a  number  of  organic  compounds,  where  the 
value  of  i  is  unity.  A  few  examples  from  each  class  of 
compounds  will  be  given,  since  it  is  a  matter  of  the  very 
greatest  importance  to  determine  whether  the  two  values 
of  i  agree.  If  they  do,  the  theory  just  advanced  is  made 
quite  probable.  If  they  do  not,  it  is  almost  a  conclusive 
argument  against  the  correctness  of  the  theory. 

BASES 

SUBSTANCE  £=—?—  i=i+(k  —  i)  a 

18.5 

Barium  hydroxide,       Ba(OH)2  2.69  2.67 

Strontium  hydroxide,   Sr(OH)2  2.61  2.72 

Calcium  hydroxide,      Ca(OH)2  2.59  2.59 

Sodium  hydroxide,       NaOH  1.96  1.88 

Potassium  hydroxide,  KOH  1.91  1.93 

Ammonia,  NH3  1.03  i.oi 

Methylamine,  CH3NH2  i.oo  1.03 

Trimethylamine,  (CH3)3N  1.09  1.03 

Ethylamine,  C2H5NH2  i.oo  1.04 

Aniline,  C6H5NH2  0.83  i.oo 

1  Harper's  Science  Series,  IV.  49. 


THEORY  OF  ELECTROLYTIC  DISSOCIATION 


99 


ACIDS 


Hydrochloric  acid, 
Hydrobromic  acid, 
Nitric  acid, 
Chloric  acid, 
Sulphuric  acid, 
Sulphurous  acid, 
Formic  acid, 
Acetic  acid, 
Tartaric  acid, 
Malic  acid, 
Lactic  acid, 


HC1 

1.98 

1.90 

HBr 

2.03 

1.94 

HNO3 

1.94 

1.92 

HC1O3 

1.97 

1.91 

H2S04 

2.06 

2.19 

H2S03 

1.03 

1.28 

HCOOH 

1.04 

1.03 

CH3COOH 

1.03 

I.OI 

C4H606 

1.05 

I.  II 

C4H605 

i.  08 

1.07 

C3H603 

I.OI 

1.03 

SALTS 


SUBSTANCE 

Potassium  chloride, 
Sodium  chloride, 
Ammonium  chloride, 
Potassium  cyanide, 
Potassium  nitrate, 
Potassium  acetate, 
Silver  nitrate, 
Potassium  sulphate, 
Ammonium  sulphate, 
Barium  chloride, 
Strontium  chloride, 
Calcium  chloride, 
Barium  nitrate, 
Strontium  nitrate, 
Calcium  nitrate, 
Mercuric  chloride, 
Cadmium  nitrate, 


•=-f-  «  =  x+(*-i)a 


KC1 

1.82 

1.86 

NaCl 

1.90 

1.82 

NH4C1 

1.88 

1.84 

KCN 

1.74 

1.88 

KN03 

1.67 

1.81 

CH3COOK 

1.86 

1.83 

AgN03 

i.  60 

1.86 

K2S04 

2.  II 

2-33 

(NH4)2S04 

2.OO 

2.17 

BaCl2 

2.63 

2-54 

SrCl2 

2.76 

2.50 

CaCl2 

2.70 

2.50 

Ba(N03)2 

2.19 

2-13 

Sr(N03)2 

2.23 

2.23 

Ca(N03)2 

2.O2 

2-33 

HgCl2 

I.  II 

1.05 

Cd(N03)2 

2.32 

2.46 

100  ELECTROLYTIC  DISSOCIATION 

ORGANIC  COMPOUNDS 


Methyl  alcohol, 

CH40 

0.94 

Ethyl  alcohol, 

C2H60 

0.94 

Butyl  alcohol, 

C4H100 

o.93 

Mannite, 

C6H1406 

0.97 

Invert  sugar, 

C6H12O6 

1.04 

Cane-sugar, 

C^HaOn 

1.  00 

Phenol, 

C6H60 

0.84 

Acetone, 

C3H60 

0.92 

1. 00 
1. 00 
1. 00 
1. 00 
1. 00 
1. 00 
1. 00 
1. 00 


That  there  is  a  general  agreement  between  the  two  val- 
ues of  i,  in  the  above  tables,  is  evident.  That  there  are 
some  discrepancies,  is  just  what  would  be  expected,  from 
the  experimental  errors  contained  in  both  the  freezing- 
point  and  the  conductivity  methods.  It  must  be  further 
borne  in  mind,  that  the  freezing-point  method  was  very 
imperfectly  developed  when  the  above  determinations  were 
made. 

Another  cause  of  these  discrepancies  was  pointed  out 
by  Arrhenius,  as  follows  :  — 

"  There  is  one  condition  which  interferes,  possibly  very 
seriously,  with  directly  comparing  the  figures  in  the  last 
two  columns ;  namely,  that  the  values  really  hold  for  differ- 
ent temperatures.  All  the  figures  in  next  to  the  last  col- 
umn hold,  indeed,  for  temperatures  only  a  very  little  below 
o°  C,  since  they  were  obtained  from  experiments  on  in- 
considerable lowerings  of  the  freezing-point  of  water.  On 
the  other  hand,  the  figures  of  the  last  column  for  acids  and 
bases  (Ostwald's  experiments)  hold  at  25°,  the  others  at 
1 8°.  The  figures  of  the  last  column  for  non-conductors 
hold,  of  course,  also  at  o°  C,  since  these  substances,  at  this 


THEORY  OF  ELECTROLYTIC   DISSOCIATION  IOI 

r 

temperature,  do  not  consist,  to  any  appreciable  extent,  of 
dissociated  (active)  molecules."  1 

Arrhenius  then  refers  to  the  general  agreement  between 
the  two  sets  of  values  in  the  following  terms  :  — 

"An  especially  marked  parallelism  appears,  beyond 
doubt,  on  comparing  the  figures  in  the  last  two  columns. 
This  shows  a  posteriori,  that  in  all  probability  the  assump- 
tions on  which  I  have  based  the  calculation  of  these  figures 
are,  in  the  main,  correct.  These  assumptions  were  :  — 

"i.  That  van't  Hoff's  law  holds  not  only  for  most,  but 
for  all,  substances,  even  for  those  which  have  hitherto  been 
regarded  as  exceptions  (electrolytes  in  aqueous  solution). 

"  2.  That  every  electrolyte  (in  aqueous  solution)  consists 
partly  of  active,  (in  chemical  and  electrical  relation)  and 
partly  of  inactive,  molecules,  the  latter  passing  into  active 
molecules  on  increasing  the  dilution,  so  that  in  infinitely 
dilute  solutions  only  active  molecules  exist.  Arrhenius 
then  calls  attention  to  the  difference  between  the  kind  of 
dissociation  indicated  here,  and  that  shown  when  a  vapor- 
like  ammonium  chloride  dissociates  by  heat. 

"  Although  the  dissolved  substance  exercises  an  osmotic 
pressure  against  the  wall  of  the  vessel,  just  as  if  it  were 
partly  dissociated  into  its  ions,  yet  the  dissociation  with 
which  we  are  here  dealing  is  not  exactly  the  same  as  that 
which  exists  when,  e.g.,  an  ammonium  salt  is  decomposed 
at  a  higher  temperature.  The  products  of  dissociation  in 
the  first  case  (the  ions)  are  charged  with  very  large  quan- 
tities of  electricity,  of  opposite  kind,  whence  certain  condi- 
tions appear  (the  incompressibility  of  electricity),  from 
which  it  follows  that  the  ions  cannot  be  separated  from 

i  Harper's  Science  Series,  IV,  54:,  ^  •> 


102  ELECTROLYTIC  DISSOCIATION 

one  another  to  any  great  extent  without  a  large  expendi- 
ture of  energy.  On  the  contrary,  in  ordinary  dissociation, 
where  no  such  conditions  exist,  the  products  of  dissociation 
can,  in  general,  be  separated  from  one  another."  1 

Although  Arrhenius  pointed  out,  so  clearly,  the  charac- 
teristic feature  of  the  dissociation  which  he  believed  elec- 
trolytes to  undergo  in  the  presence  of  water,  namely,  that 
the  products  of  dissociation  were  charged,  the  one  always 
positively,  the  other  always  negatively,  yet  this  has  often 
been  overlooked. 

Summary.  —  In  concluding  this  chapter,  we  will  briefly 
recall  the  steps  which  led  to  the  theory  of  electrolytic  dis- 
sociation. The  stages  by  which  van't  Hoff  passed  from 
the  study  of  the  position  of  atoms  in  space  to  Pfeffer's 
work  on  osmotic  pressure  have  been  followed  in  detail. 
Van't  Hoff  showed,  from  Pfeffer's  results,  and  also  theoreti- 
cally, that  the  laws  of  Boyle,  Gay  Lussac,  and  Avogadro, 
for  gas  pressure,  apply  to  the  osmotic  pressure  of  solutions. 

But  these  apply  only  to  solutions  of  non-electrolytes,  i.e. 
substances  which,  when  in  the  presence  of  water,  do  not 
conduct  the  current.  All  electrolytes,  i.e.  the  acids,  bases, 
and  salts,  are  exceptions,  showing  greater  osmotic  pressure 
than  would  accord  with  the  laws  of  gas  pressure.  To  what 
w.as  this  discrepancy  due  ?  v  Since  osmotic  pressure  is 
proportional  to  the  number  of  parts  present,  too  great 
osmotic  pressure  means  more  parts  present  than  would 
be  expected. 

In  order  that  we  might  have  more  parts  present  than 
the  molecules,  it  is  necessary  that  the  molecules  should 
undergo  decomposition.  How  is  it  possible  to  think  of 

of*  ,4  Harper's -Science  Aeries,  IV,  54. 


THEORY  OF  ELECTROLYTIC  DISSOCIATION  103 

stable  molecules,  such  as  hydrochloric  acid,  potassium 
hydroxide,  potassium  chloride,  suffering  decomposition  ? 
Arrhenius  furnished  the  answer.  He  had  resort  to  the 
old  theory  proposed  by  Clausius,  to  account  for  electrol- 
ysis, that  in  the  presence  of  water  the  molecules  are 
broken  down  into  ions.  Arrhenius  pointed  out  two  ways 
of  calculating  the  amount  of  this  dissociation,  the  one 
based  on  conductivity,  the  other  on  freezing-point  lower- 
ing, and  showed  that  the  results  from  the  two  methods 
agreed. 

All  of  the  compounds  which  give  abnormally  great 
osmotic  pressure,  and  are  therefore  dissociated  into  ions, 
conduct  the  current  when  in  solution  in  water,  and  are 
therefore  electrolytes.  This  kind  of  dissociation  has  come 
to  be  known  as  electrolytic,  and  the  theory  advanced  by 
Arrhenius  as  the  Theory  of  Electrolytic  Dissociation. 

It  is  one  thing  to  propose  a  theory,  and  another  to  pro- 
pose a  theory  which  is  true.  In  the  next  chapter  we  will 
consider  some  of  the  lines  of  evidence  bearing  upon  the 
theory  of  electrolytic  dissociation. 


CHAPTER   III 

EVIDENCE  BEARING  UPON  THE    THEORY  OF   ELECTROLYTIC 
DISSOCIATION 

THE    PHYSICAL     PROPERTIES    OF     COMPLETELY    DISSOCIATED 
SOLUTIONS    SHOULD    BE   ADDITIVE 

A  theory  in  science  must,  first  of  all,  be  capable  of 
experimental  test.  If  it  cannot  be  shown  to  be  either  true 
or  false,  it  is  of  little  value  as  a  scientific  generalization. 

Arrhenius  pointed  out  in  his  first  paper,  that  evidence 
bearing  upon  his  theory  could  be  obtained  from  a  study  of 
the  physical  properties  of  solutions,  whose  dissociation,  in 
terms  of  the  theory,  was  supposed  to  be  complete.  "  If  a 
salt  (in  aqueous  solution)  is  completely  broken  down  into 
its  ions,  most  of  the  properties  of  this  salt  can,  of  course, 
be  expressed  as  the  sum  of  the  properties  of  the  ions ;  since 
the  ions  are  independent  of  one  another  in  most  cases,  and 
since  every  ion  has  therefore  a  characteristic  property, 
independent  of  the  nature  of  the  opposite  ion  with  which 
it  occurs." 

He  also  observed  that  we  rarely  have'  to  do  with  com- 
pletely dissociated  solutions.  Those  of  the  salts,  strong 
acids,  and  strong  bases,  are  dissociated  only  from  80  to  90 
per  cent,  at  ordinary  dilutions,  and  the  additive  nature  of 
the  properties  of  even  such  solutions  would  be  only  ap- 
proximate. Another  class  of  substances,  such  as  mercuric 

104 


EVIDENCE  FOR  THE  THEORY  I  OS 

chloride,  cadmium  iodide,  and  all  of  the  weak  acids 
and  bases,  organic  and  inorganic,  are  comparatively  lit- 
tle dissociated  by  water  at  moderate  dilutions,  and  the 
physical  properties  of  solutions  of  these  substances  are 
not  those  of  the  ions  alone,  but  of  both  ions  and 
molecules. 

The  point,  in  a  word,  is  this :  The  physical  properties  of 
completely  dissociated  solutions  must  be  a  function  of  the 
physical  properties  of  the  ions,  as  there  are  no  mole- 
cules present.  Since  each  ion  has  its  own  specific  prop- 
erties, independent  of  the  nature  of  the  other  ion  with 
which  it  is  associated,  the  physical  properties  of  com- 
pletely dissociated  solutions  must  be  the  sum  of  the 
physical  properties  of  the  ions  in  those  solutions.  If  the 
solutions  are  not  completely  dissociated,  their  properties 
are  those  both  of  the  ions  and  of  the  molecules. 

We  must  now  study  the  physical  properties  of  com- 
pletely dissociated  solutions,  and  see  what  relations  exist 
between  these  and  the  physical  properties  of  the  ions  which 
they  contain.  We  will  take  solutions  of  salts. 

Specific  Gravity  of  Salt  Solutions.  —  If  a  salt  is  added 
to  water,  the  volume  of  the  solution  is  different  from  that 
of  the  pure  solvent,  and  also  from  the  sum  of  the  volumes 
of  the  liquid  and  the  solid.  If  the  resulting  solution  is 
very  dilute,  the  salt  is  completely  dissociated  into  its  ions. 
Nernst1  has  shown,  from  the  results  of  J.  Traube,2  that 
the  change  in  volume  under  such  conditions  is  an  additive 
property  of  the  ions.  Given  a  solution  containing  a 
gram-molecular  weight  of  a  salt  whose  molecular  weight 
is  M,  in  m  grams  of  water.  Let  the  specific  gravity  of 

1  Theoretische  Chemie,  p.  317.  2  Ztschr.  anorg.  Chem.,  3,  i. 


IO6  ELECTROLYTIC  DISSOCIATION 

the  solution  be  S,  the  specific  gravity  of  water  s.     The 
change  in  volume  Az/,  on  dissolving  the  salt,  will  be :  — 

A        M+m     m 
S          s' 

The  following  results  are  given  :  — 

KC1  =  26.7  NaCl  =  17.7 

KBr  =  35.1  NaBr  =  26.7 

KI    =45.4  Nal    =36.1 

f  KBr    -  KC1    =  8.4  1  f  KI    -  KBr    =  10.3  J 

{  NaBr  -  NaCl  =  9.0  J  {  Nal  -  NaBr  =    9.4! 


[KI   -KC1 

I  Nal  -  NaCl 


=  18.7! 
=  18.4  J 


KC1  -  NaCl  =  9.0 
KBr  -  NaBr  =  8.4 
KI  -Nal  =9.3 


These  results  show  the  additive  nature  of  the  specific 
gravity  of  salt  solutions.  The  difference  between  the 
chlorine  and  the  bromine  ions  is  about  8.7;  between 
chlorine  and  iodine  18.5;  between  bromine  and  iodine 
9.8;  while  between  potassium  and  sodium  it  is  about  9.0. 

The  additive  nature  of  the  specific  gravity  of  salt  solu- 
tions had,  indeed,  been  pointed  out  much  earlier  by 
Valson.1  He  had  shown  exactly  what  is  brought  out 
above :  Given  salt  solutions  of  comparable  concentration, 
i.e.  containing  say  a  gram-molecule  of  the  salt  per  litre, 
the  difference  between  the  specific  gravities  of  solutions 
containing  two  metals  combined  with  the  same  acid  is 
constant,  whatever  the  nature  of  the  acid.  Similarly,  the 
difference  between  the  specific  gravities  of  two  salts  of 
the  same  acid  with  any  metal  is  constant,  regardless  of 

1  Compt.  rend.,  73,  441  (1874). 


EVIDENCE   FOR  THE  THEORY 

the  nature  of  the  metal.  The  specific  gravity  of  a  salt 
solution  is,  then,  obtained  by  adding  to  a  constant  number 
two  values,  —  the  one  for  the  acid,  the  other  for  the 
metal.  These  values  Valson  termed  "  moduli "  ;  and  he 
worked  out  their  values  for  a  large  number  of  elements. 

Valson l  concluded  from  his  work,  that  the  molecules  of 
salts  must  be  completely  broken  down  in  solution.  But 
the  evidence  in  favor  of  such  a  view  was  not  strong 
enough  at  that  time  to  bring  it  into  favor. 

Change  of  Volume  in  Neutralization.  —  The  change  of 
volume  produced  by  neutralizing  acids  with  bases  has 
been  extensively  studied  by  Ostwald.2  The  solutions 
contained  a  gram-equivalent  of  the  acid  or  base,  in 
a  kilogram,  and  were,  therefore,  not  completely  disso- 
ciated ;  so  that,  if  the  change  in  volume  was  addi 
tive,  it  would  be  shown  only  approximately  by  such 
solutions. 

Ostwald3  worked  with  nineteen  acids,  including  the 
strongest  mineral  acids,  and  some  of  the  more  strongly 
dissociated  organic  acids.  He  neutralized  these  with  the 
three  bases,  potassium,  sodium,  and  ammonium.  A  few 
of  his  results  are  given,  the  change  in  volume  being  ex- 
pressed in  cubic  centimetres.  The  differences  in  the  hori- 
zontal lines  are  the  differences  between  potassium,  sodium, 
and  ammonium,  in  combination  with  the  same  acid.  The 
differences  in  the  vertical  columns  are  the  differences 
between  the  different  acids  in  combination  with  the  same 
bases,  obtained  by  subtracting  the  value  for  the  acid  from 
the  value  for  nitric  acid. 

l  Compt.  rend.,  73,  441 ;  74,  103 ;  75,  1033.  2  Journ.  prakt.  Chem.  [2] ,  18,  353. 

3  Lehrb.  d.  allg.  Chem.  I,  p.  788. 


108  ELECTROLYTIC  DISSOCIATION 

POTASSIUM  SODIUM  AMMONIUM 

HYDROXIDE  HYDROXIDE  HYDROXIDE 

Nitric  acid,  20.05  (0.28)     19.77  (26.21)  —    6.44  (26.49) 

(o.53)  (o-53)  (o-i3) 

Hydrochloric  acid,  19.52  (0.28)     19.24  (25.81)  —    6.57  (26.09) 

(7.69)  (7-61)                    (7-15) 

Formic  acid,            12.36  (0.20)  12.16  (25.75)  —13.59  (25.95) 

(10.53)  (10.49)                    (9-82) 

Acetic  acid,               9.52  (0.24)  9.28  (25.54)  —  16.26  (25.78) 

(8.i5)        (8.29)          (7.91) 

Sulphuric  acid,  '      11.90  (0.42)     11.48  (25.83)  —  14.35  (26.25) 

(11.82)  (11.84)  (".19) 

Succinic  acid,  8.23  (0.30)       7.93  (25.56)   -17.63  (25.86) 

If  we  take  the  perpendicular  rows  in  parentheses,  we  find 
very  nearly  a  constant  difference  for  the  strong  acids  and 
bases.  Similarly,  if  we  take  the  horizontal  rows  in  paren- 
theses, we  find  very  nearly  a  constant  difference.  This 
means  that  the  difference  of  change  in  volume,  produced 
by  neutralizing  two  different  bases  by  a  given  acid,  is  a 
constant,  independent  of  the  nature  of  the  acid ;  and, 
similarly,  the  difference  of  the  change  in  volume  on  neu- 
tralizing two  different  acids  by  a  given  base,  is  independent 
of  the  nature  of  the  base. 

The  change  in  volume,  when  acids  and  bases  neutralize 
each  other,  like  the  specific  gravity  of  salt  solutions,  is, 
then,  an  additive  property,  depending  both  upon  the  nature 
of  the  acid  and  of  the  base ;  and  we  could  work  out  here, 
as  Valson  has  done  in  the  case  of  specific  gravities,  the 
numerical  values  of  the  constants  for  each  constituent. 

Specific  Refractive  Power  of  Salt  Solutions.  —  Gladstone 
calculated  the  refraction  equivalents  R,  of  a  number  of  ele- 
ments, from  the  formula :  — 


EVIDENCE   FOR  THE  THEORY  1 09 

~d 

in  which  P  is  the  weight  of  the  substance,  n  the  index  of 
refraction,  and  d  the  density.  He  also  showed  that  the 
refraction  coefficients  of  salts  were  the  sum  of  the  refrac- 
tion equivalents  of  the  elements. 

That  this  is  true  is  seen  from  the  following  table  of  re- 
sults, taken  by  Arrhenius 1  from  the  Lehrbuch  of  Ostwald.2 
Only  a  few  examples  are  given  here. 

HYDROGEN  *   POTASSIUM  SODIUM 

Chloride,  14.44  (4-<>o)  18.44  (3-3>  I5-11 

(6.2)  (6.9)  (6.6) 

Bromide,  20.63  (4-7)  25-34  (3-6)  21.70 

(3-4)  (3-5)  (3-0) 

Nitrate,  17.24  (4.6)  21.80  (3.1)  18.66 

(4-0)  (5.8)  (5.4) 

Acetate,  21.20  (6.4)  27.65  (3.6)  24.05 

(24.0)  (30.0)  (26.4) 

Tartrate,     45.18  (12.4)             57.60  (7.2)           50.39 

The  differences,  both  horizontally  and  vertically,  are  as 
constant  as  could  be  expected,  except  for  the  two  organic 
acids  which,  at  the  dilutions  employed,  are  only  slightly 
dissociated.  This  means  that  the  different  effect  of  potas- 
sium and  hydrogen,  on  the  refraction  equivalent,  is  con- 
stant, whatever  the  acid  with  which  they  are  combined,  and 
the  same  holds  for  potassium  and  sodium.  Also,  that  chlo- 
rine, bromine,  etc.,  have  a  constant  effect  on  the  refractive 
power,  whether  they  are  combined  with  hydrogen,  potas- 
sium, or  sodium.  In  a  word,  the  refractive  power  of  salt 

1  Ztschr.  phys.  Chem.,  i,  645.     Harper's  Science  Series,  IV,  62. 

2  Lehrb.  d.  allg.  Chem.,  II,  p.  446. 


1 10  ELECTROLYTIC  DISSOCIATION 

solutions  is  distinctively  an  additive  property  of  the  con- 
stituents. 

Rotatory  Power  of  Salt  Solutions.  —  The  power  possessed 
by  solutions  of  some  salts  to  rotate  the  plane  of  polariza- 
tion of  light,  must  be  a  property  of  the  optically  active  con- 
stituent  of  the  salt,  or,  if  both  constituents  are  optically 
active,  it  must  be  the  sum  of  the  activities  of  the  two. 
Oudemans1  has  shown  that  optically  active  bases,  such  as 
the  monacid  alkaloids,  produce  the  same  rotation,  regard- 
less of  the  nature  of  the  pptically  inactive  acid  with  which 
they  are  combined.  And  optically  active  acids  rotate  the 
plane  of  polarization,  independent  of  the  nature  of  the  inac- 
tive base  combined  with  them.  This  is  very  well  shown 
by  the  work  of  Hartmann,2  on  the  salts  of  camphoric  acid. 

Li2        Mg         (NH4)2        Ca         Na2        K2        Ba 
37-5       39-5  38.4          39-1       36.o      36.1      36.5 

The  rotatory  power  of  salts  of  this  acid  is  practically 
constant,  independent  of  the  nature  of  the  base  combined 
with  it. 

The  Color  of  Salt  Solutions. — The  absorption  which  light 
undergoes,  in  passing  through  a  solution  of  a  completely 
dissociated  substance  must,  in  terms  of  our  theory,  be  the 
sum  of  the  absorption  of  the  cation,  plus  that  of  the  anion. 
If  one  of  the  ions  is  colorless,  the  absorption  must  be 
entirely  that  of  the  other  ion. 

That  this  is  qualitatively  true  is  a  matter  of  common 
experience.  We  utilize  the  color  of  solutions  to  determine 
the  nature  of  their  constituents.  Thus,  cupric  salts  in  di- 
lute aqueous  solutions  are  blue,  or  bluish  green,  regardless 

1  Beibl.,  Q,  635.  2  Ber.  d.  chem.  Gesell.  (1888),  221. 


EVIDENCE  FOR  THE  THEORY  III 

of  the  chemical  nature  of  the  anion  with  which  the  copper 
is  combined,  provided  that  it  is  colorless.  Likewise,  the 
chromates  are  yellow,  and  the  salts  of  nickel  green. 

A  method  for  determining,  quantitatively,  whether  the 
absorption  of  light  is  additive,  is  to  prepare  a  number  of 
salts  of  an  acid  whose  anion  is  colored,  the  cation  being 
always  colorless.  Then  determine  whether  all  of  the  salts 
have  the  same  absorption  spectrum.  The  metallic  salts 
of  permanganic  acid  are  particularly  well  adapted  to  this 
purpose,  and  they  have  been  thoroughly  studied  by 
Ostwald1  in  this  connection.  These  salts  show  five 
absorption  bands  in  the  yellow  and  green,  and  four  of 
these  have  been  measured  by  Ostwald  for  thirteen  salts 
of  permanganic  acid.  The  results  are  so  striking,  that 
they  are  given  in  the  following  table  :  — 

PERMANGANATES.     ABSORPTION  BANDS. 

I  II  III  IV 

Hydrogen,  2601  ±  0.5  2698  ±  0.8  2804  ±0.7  2913  ±  1.7 
Potassium,  2600  ±  1.3  2697  ±  o.i  2803  ±  0.9  2913  ±  i.i 
Sodium,  2602  ±  1.2  2698  ±0.8  2803  ±  0.7  2913  ±0.8 

Ammonium,       2601  ±  1.3     2698  ±  1.4     2802  ±  o.i     2913  ±  o.i 
Lithium, 
Barium, 
Magnesium, 
Aluminium, 
Zinc, 
Cobalt, 
Nickel, 

Cadmium,  2600  ±  o.i  2700  ±0.2  2803  ±  0.8  2913  ±  1.4 
Copper,  2602  ±  1.2  2699  ±0.1  2803  ±0.9  2913  ±0.8 

1  Ztschr.  phys.  Chem.,  9,  584. 


112  ELECTROLYTIC  DISSOCIATION 

From  these  results,  Ostwald  concluded  that  the  absorp- 
tion spectra  of  the  thirteen  permanganates  are  just  the 
same. 

A  large  number  of  other  compounds  were  investigated,1 
including  ten  salts  of  fluoresce'fn,  ten  of  eosin  yellow,  ten 
of  eosin  blue,  ten  of  iodoeosin,  ten  of  dinitrofluorescem, 
rosolic  acid,  and  a  number  of  other  substances.  Also  a 
large  number  of  cases  were  studied,  where  a  colored  cation 
was  combined  with  a  number  of  colorless  anions.  Thus, 
the  salts  of  pararosaniline  with  twenty  colorless  acids, 
and  an  equal  number  of  the  salts  of  aniline  violet,  were 
investigated. 

Ostwald  studied,  in  all,  about  three  hundred  cases,  to 
determine  whether  the  color  of  a  solution  with  one  colored 
ion  is  effected  at  all  by  the  presence  of  the  colorless  ion. 
He  concluded  that  salts  with  one  and  the  same  colored  ion, 
in  dilute  solution,  always  show  exactly  the  same  absorp- 
tion spectra. 

The  elaborate  investigation  just  considered  shows  con- 
clusively, that  the  color  of  salt  solutions  is  exactly  the  color 
of  the  colored  ion,  and  from  this  it  follows,  that  if  both 
ions  were  colored,  the  color  of  the  solution  would  be  the 
sum  of  the  colors  of  the  two  ions.  The  color  of  salt 
solutions  is,  therefore,  an  additive  property. 

The  use  of  indicators  in  quantitative  analysis  is  based 
upon  this  fact.  That  a  substance  may  be  used  as  an 
indicator  for  acids  and  bases,  it  is  necessary  that  one  of 
the  ions  should  have  a  different  color  from  the  molecule. 
Take  the  case  of  phenolphthalei'n.  Its  alcoholic  solution 
is  nearly  colorless,  and  since  it  does  not  conduct  the 

l  Loc.  cit. 


EVIDENCE  FOR  THE  THEORY  113 

current,  it  is  undissociated.  The  molecules  of  phenol- 
phthalei'n  are,  therefore,  colorless.  If  we  add  an  alkali,  say 
sodium  hydroxide,  to  phenolphthalei'n,  the  sodium  salt  is 
formed ;  but  this  dissociates  at  once  into  the  cation  sodium, 
and  the  complex  organic  anion,  which  is  deeply  colored. 
The  characteristic  color  of  phenolphthalei'n,  acting  as  an 
indicator  for  an  alkali,  is,  then,  always  the  color  of  the 
complex  anion.  If  to  the  colored  solution  a  little  acid  is 
added,  the  original  phenolphthalem  is  formed,  and  is 
colorless. 

Take,  on  the  other  hand,  the  basic  indicator,  cyanine; 
the  molecules  of  the  free  base  are  blue.  It  is  a  weak 
base,  and,  therefore,  but  little  dissociated.  Add  acid ;  the 
salt  is  formed,  which  at  once  dissociates.  The  complex 
organic  cation  is  colorless,  and,  hence,  on  adding  acid,  the 
color  due  to  the  molecules  of  the  free  base  disappears. 
This  is  exactly  the  opposite  of  the  case  first  considered. 

Finally,  take  methyl  orange,  where  the  molecules  are  red. 
Add  a  base,  the  salt  is  formed,  and  this  breaks  down  at 
once  into  ions.  The  color  of  the  complex  organic  anion 
is,  in  this  case,  yellow.  The  addition  of  acid,  therefore, 
brings  out  the  characteristic  red  color  of  this  indicator. 

A  number  of  other  cases  might  be  taken  up,  where  the 
molecule  is  either  colorless,  or  has  a  different  color  from 
one  of  its  ions,  but  the  cases  considered  are  typical,  and 
suffice  to  make  the  point  clear. 

A  Demonstration  of  the  Dissociating  Action  of  Water.  — 
Jones  and  Allen1  have  worked  out  a  color  demonstration 
of  the  dissociating  action  of  water,  which  is  based  upon 
the  principle  of  indicators  just  considered.  If,  to  an 

1  Amer.  Chem.  Journ.,  18,  377. 

I 


114  ELECTROLYTIC  DISSOCIATION 

alcoholic  solution  of  phenolphthalem,  a  few  drops  of 
aqueous  ammonia  are  added,  there  is  no  sign  of  the  red 
color  of  the  indicator.  If  water  is  now  added  to  the 
alcoholic  solution,  the  red  color  appears.  When  potassium 
or  sodium  hydroxide  is  substituted  for  ammonia,  the  red 
color  appears  at  once,  without  the  addition  of  water. 
There  is,  thus,  a  marked  difference  between  potassium 
and  sodium  hydroxide  and  ammonium  hydroxide. 

It  would  be  difficult  to  interpret  these  facts  without  the 
aid  of  the  theory  of  electrolytic  dissociation.  In  the  light 
of  this  theory  they  are  perfectly  intelligible. 

When  a  few  drops  of  aqueous  ammonia  are  added  to 
several  cubic  centimetres  of  alcohol,  little  or  no  dissociation 
of  the  ammonium  hydroxide  is  effected.  The  addition  of 
water  dissociates  the  base,  the  degree  of  dissociation  de- 
pending upon  the  amount  of  water  present  with  respect  to 

+ 
alcohol.     The  presence  of  the  ions  NH4  and  OH  would 

cause  the  phenolphthalei'n  to  dissociate.  The  complex 
anion  gives  its  characteristic  color  to  the  solution  in 
which  it  is  present.  The  hydrogen  and  hydroxyl  ions 
would  then  combine  and  form  water. 

It  is  possible  tfiat  the  actual  course  of  the  reaction  is 
somewhat  different  from  that  just  described.  It  may  be 
that  the  ammonium  group  first  combines  with  the  phenol- 
phthalem in  the  alcoholic  solution.  The  addition  of  water 
would  then  dissociate  this  compound,  giving  the  colored 
anion  referred  to  above. 

The  dissociation  theory  furnishes  this  explanation.  It 
remains  to  determine  whether  the  explanation  is  true. 

If  it  is,  then  a  solution,  formed  by  adding  a  little  aqueous 
ammonia  to  a  considerable  volume  of  alcohol,  should  show 


EVIDENCE  FOR  THE  THEORY  H5 

little  or  no  dissociation,  and  the  amount  of  the  dissociation 
should  increase  with  the  addition  of  water.  Solutions  of 
potassium  or  sodium  hydroxide,  in  mixtures  of  alcohol 
and  water,  should  be  more  dissociated  than  corresponding 
solutions  of  ammonium  hydroxide.  Indeed,  a  solution  of 
sodium  or  potassium  hydroxide,  in  alcohol  alone,  should 
manifest  some  dissociation,  since,  as  stated  above,  it  gives 
the  color  reaction  with  phenolphthalem. 

All  of  these  points  were  tested,  experimentally,  by  the 
conductivity  method,  with  the  result  that  the  theory  of 
electrolytic  dissociation  was  entirely  confirmed. 

This  experiment  furnishes  a  satisfactory  lecture  demon- 
stration of  the  dissociating  action  of  water.  A  few  drops 
of  an  alcoholic  solution  of  phenolphthalem  are  placed  in  a 
glass  cylinder,  and  diluted  to,  say,  50  cc.  by  the  addition  of 
alcohol.  A  few  drops  of  an  aqueous  solution  of  ammonia 
are  then  added.  A  red  color  may  appear  where  the 
aqueous  ammonia  first  comes  in  contact  with  the  alcoholic 
solution  of  phenolphthalem,  but  this  will  disappear,  in- 
stantly, on  shaking  the  cylinder,  leaving  the  solution  with 
a  yellowish  tint,  possibly  due  to  the  formation  of  the 
ammonium  salt  of  phenolphthalem.  Water  is  then  gradu- 
ally added  to  the  cylinder,  when  the  red  color  will  appear, 
at  first  faint,  then  stronger,  as  the  amount  of  water 
increases.  When  the  red  color  has  become  intense, 
add  a  considerable  volume  of  alcohol,  and  the.  entire 
color  will  disappear,  leaving  the  solution  slightly  yellow 
again. 

The  experiment  serves,  then,  not  only  to  illustrate  the 
dissociating  action  of  water,  but  the  driving  back  of  the 
ions  into  molecules  by  alcohol. 


Il6  ELECTROLYTIC  DISSOCIATION 

Conductivity  is  Additive.      The  Law  of  Kohlrausch.  — 

It  has  been  shown  by  Kohlrausch,  that  the  conductivity  of 
solutions  of  electrolytes  is  an  additive  property  of  the  ions 
which  take  part  in  carrying  the  current.  Indeed,  the  law 
of  Kohlrausch,  of  the  independent  migration  velocity  of 
the  ions,  is  but  another  expression  of  this  fact.  It  is  well 
known  that  the  law,  in  the  form  stated  by  Kohlrausch, 
holds  only  for  great  dilutions,  in  which  dissociation  is  com- 
plete. Ostwald1  has  pointed  out  that  the  law  holds  for  any 
dilution,  provided  that  we  take  into  account  the  amount  of 
the  dissociation  at  that  dilution.  This  is  obviously  neces- 
sary, since  it  is  only  the  dissociated  molecules  which  take 
part  in  the  conductivity.  If  we  represent  the  percentage 
of  dissociation,  or  the  activity  coefficient,  by  «,  the  law  of 
Kohlrausch  becomes :  — 

/&=«(#+.«>), 

u  depending  upon  the  cation,  v  upon  the  anion.  The  law 
in  this  form  is  applicable  to  all  solutions  of  electrolytes, 
and  illustrates,  also,  the  additive  property  of  conduc- 
tivity. 

A  number  of  other  properties  could  be  adduced  in 
evidence  of  the  general  principle,  that  the  properties  of 
completely  dissociated  solutions  are  additive,  being  the 
sum  of  the  properties  of  the  ions ;  but  those  already  con- 
sidered are  quite  sufficient.  The  theory  of  electrolytic 
dissociation  is  here  entirely  substantiated  by  the  facts. 
And  these  facts  would  be  very  difficult  to  explain  without 
some  such  conception  as  that  with  which  we  are  now 
dealing. 

l  Lehrb.  d.  allg.  Chem.  II,  p.  673. 


EVIDENCE  FOR  THE  THEORY  1  17 

PROPERTIES    OF    COMPLETELY   DISSOCIATED,   AND    OF   UNDIS- 
SOCIATED    MIXTURES 

Mixture  of  Two  Completely  Dissociated  Compounds.  — 

The  theory  of  electrolytic  dissociation  leads  to  some  inter- 
esting conclusions,  in  the  case  of  mixtures  of  completely 
dissociated  substances,  and  these  conclusions  can  be  tested 
experimentally.  Let  us  take  the  case  of  two  salts  which 
are  completely  dissociated  at  moderate  dilutions,  say,. 
sodium  chloride  and  potassium  bromide.  We  would  have 
in  the  solution  only  the  ions  into  which  these  compounds 
had  dissociated  :  — 


KBr   =  K  +  Br. 

We  would  have  sodium  and  potassium  cations,  and  chlorine 
and  bromine  anions.  All  the  properties  of  such  a  mixture 
would  be  a  function  of  the  properties  of  these  ions. 

Suppose  we  were  now  to  prepare  a  mixture  of  potassium 
chloride  and  sodium  bromide,  which  was  completely  dis- 
sociated. We  would  have  in  the  solution  :  — 

KC1    =  K  +C1; 
NaBr  =  Na  +  Br, 

potassium  and  sodium  cations,  and  chlorine  and  bromine 
anions.  But  these  are  exactly  the  same  ions  which  we 
had  in  our  first  mixture. 

We  are  led  to   the   conclusion,  that   if   we  use  gram- 


Il8  ELECTROLYTIC  DISSOCIATION 

molecular  weights  of  both  substances  in  each  case,  we 
will  have  exactly  the  same  number  of  the  same  kinds  of 
ions  in  the  two  solutions.  And  since  the  properties  of  a 
completely  dissociated  solution  depend  only  upon  the 
properties  of  the  ions  present,  the  properties  of  these  two 
mixtures  must  be  the  same.  If,  then,  we  mix  a  gram- 
molecular  weight  of  sodium  chloride  with  a  gram-molecu- 
lar weight  of  potassium  bromide,  and  dilute  the  solution  of 
the  two  until  both  are  completely  dissociated,  this  mix- 
ture must  have  exactly  the  same  properties  as  that  pre- 
pared by  mixing  a  gram-molecular  weight  of  potassium 
chloride  with  a  gram-molecular  weight  of  sodium  bro- 
mide, and  diluting  the  solution  to  the  same  point  as  the 
first.  This  is  the  conclusion  to  which  we  are  led  by  our 
theory.  What  are  the  facts?  The  facts  confirm  this 
conclusion  absolutely.  All  of  the  properties  of  the  two 
mixtures  have  been  found  to  be  exactly  the  same.  The 
two  solutions  resemble  one  another  as  closely  as  the  two 
halves  of  the  same  solution. 

Mixture  of  Two  Completely  Undissociated  Compounds.  — 
The  conclusion  to  which  we  are  led  in  the  case  of  com- 
pletely dissociated  compounds  does  not  obtain  at  all  for 
undissociated  substances.  Indeed,  in  the  latter  case,  we 
are  led  by  the  theory  to  exactly  the  opposite  conclusion. 
Take  two  undissociated  substances  —  say  methyl  chloride 
and  ethyl  bromine  —  and  dissolve  the  mixture ;  we  will 
have  only  molecules  of  the  two  substances  present.  The 
properties  of  this  mixture  will  be  a  function  of  the 
properties  of  these  two  kinds  of  molecules. 

Then,  mix  methyl  bromide  and  ethyl  chloride,  we  will 
have  only  these  two  kinds  of  molecules  present,  and 


EVIDENCE  FOR  THE  THEORY  119 

the  properties  of  the  mixture  will  be  a  function  of  the 
properties  of  the  molecules  which  are  in  the  mixture. 

But  in  the  first  mixture  we  have  molecules  of  methyl 
chloride  and  ethyl  bromide,  in  the  second,  of  methyl  bro- 
mide and  ethyl  chloride.  And  since  we  have  different 
kinds  of  molecules  in  the  two  mixtures,  the  properties  of 
the  two  must  be  different. 

If,  then,  we  mix  gram-molecular  weights  of  methyl 
chloride  and  ethyl  bromide,  the  mixture  must  have  differ- 
ent properties  from  a  corresponding  mixture  of  gram- 
molecular  weights  of  methyl  bromide  and  ethyl  chloride. 

This  is  the  conclusion  to  which  we  are  led  by  the  theory 
of  electrolytic  dissociation,  and  here  again  the  facts  are 
in  perfect  accord  with  the  theory.  It  has  been  found, 
experimentally,  that  a  mixture  of  methyl  chloride  and 
ethyl  bromide  has  properties  quite  different  from  a  corre- 
sponding mixture  of  methyl  bromide  and  ethyl  chloride. 

Fact  and  theory  thus  agree,  both  when  the  constituents 
of  the  mixture  are  completely  dissociated,  and  when  they 
are  not  at  all  dissociated. 

HEAT    OF    NEUTRALIZATION    IN    DILUTE    SOLUTIONS 

If  the  theory  of  electrolytic  dissociation  is  true,  a  dilute 
aqueous  solution  of  a  strongly  dissociated  compound  con- 
tains only  ions,  as  has  been  stated.  A  solution  of  a  base 
contains  the  hydroxyl  anion,  and  a  cation  whose  nature 
depends  upon  the  particular  base  used.  A  solution  of  an 
acid  contains  the  hydrogen  cation  and  an  anion  whose 
nature  depends  upon  the  acid  chosen.  Similarly,  a  solu- 
tion of  a  salt  is  but  a  solution  of  anions  and  cations.  In 
terms  of  the  theory  of  electrolytic  dissociation,  the  pro- 


120  ELECTROLYTIC  DISSOCIATION 

cess  of  neutralizing  an  acid  by  a  base  consists  in  the 
union  of  the  hydroxyl  anion  of  the  base  with  the  hydro- 
gen cation  of  the  acid,  forming  a  molecule  of  water.  The 
cation  of  the  base  and  the  anion  of  the  acid  remain  in 
exactly  the  same  condition  after  neutralization  as  before. 
Let  us  take  an  example. 

A  solution  of  hydrochloric  acid  is  a  solution  of  hydro- 
gen cations  and  chlorine  anions :  — 

HC1  =  H  +  Cl. 

A  solution  of  potassium  hydroxide  is  a  solution  of 
potassium  cations  and  hydroxyl  anions :  — 

KOH  =  K  +  OH. 
When  the  two  solutions  are  brought  together  we  have: — 

K  +  OH  +  H  +  Cl  =  K  +  C 1  +  H2O. 

The  potassium  and  chlorine  are  in  exactly  the  same 
condition  after  neutralization  as  before,  i.e.  both  are  ions ; 
while  the  hydrogen  and  hydroxyl  are  united,  forming  a 
molecule  of  water. 

Neutralization  of  acids  and  bases  is,  then1,  in  terms  of 
the  theory  of  electrolytic  dissociation,  nothing  more  than 
the  union  of  the  cation  hydrogen  and  the  anion  hydroxyl 
to  form  a  molecule  of  water. 

How  can  this  be  tested  experimentally? 

If  neutralization  consists  only  in  the  formation  of  a  mole- 
cule of  water,  then  the  neutralization  of  any  acid  by  any 
base  is  the  same  process  as  the  neutralization  of  any  other 


EVIDENCE  FOR  THE  THEORY  121 

acid  by  any  other  base.  Therefore,  the  heat  liberated  by 
neutralizing  an  equivalent  of  any  acid  by  an  equivalent  of 
any  base  must  always  be  the  same,  since  it  is  the  heat  of 

formation    of   the   same  amount   of  water  from  the   ions 

+ 

H  and  OH.     This  can  be  tested  directly  by  experiment. 

It  is  only  necessary  to  measure  the  heat  liberated  when 
acids  and  bases  are  neutralized,  and  see  whether  this  is 
the  same  for  the  different  compounds. 

The  following  tables  of  heats  of  neutralization  will  test 
this  point:  — 

STRONG  ACIDS  AND  BASES 

HC1     +  NaOH  =  13  700  cal.  HC1  +    LiOH        =  13700  cal. 

HBr     +  NaOH  =  13700  cal.  HC1  +    KOH         =  13700  cal. 

HNO3  +  NaOH  =  13700  cal.  HC1  + 1  Ba(OH)2  =  13800  cal. 

HI       +  NaOH  =  13800  cal.  HC1  +  £Ca(OH)2  =  13900  cal. 

WEAK  ACID  AND  STRONG  BASE 

CH3COOH  +  NaOH  =  13400  cal. 
CHC12COOH  +  NaOH  =  14830  cal. 
H3PO4  +  NaOH  =  14830  cal. 

HF  +  NaOH  =  162  70  cal. 


The  agreement  between  the  heats  of  neutralization  of 
the  strong  acids  with  the  strong  bases  is  striking,  when  we 
consider  the  necessary  errors  involved  in  thermochemical 
measurements. 

The  heats  of  neutralization  of  weak  acids  with  a  strong 
base  differ  very  greatly  from  the  constant  obtained  when 
both  compounds  are  strongly  dissociated. 


122  ELECTROLYTIC  DISSOCIATION 

In  the  application  of  the  theory  to  the  phenomenon  of 
neutralization,  it  was  assumed  above,  that  both  the  acid 
and  the  base  were  completely  dissociated.  If,  on  the 
other  hand,  either  acid  or  base  is  incompletely  dissociated, 
then  the  heat  set  free  when  the  two  are  brought  together 
is  not  simply  the  heat  liberated  by  the  union  of  hydrogen 
and  hydroxyl  ions  to  form  water,  but  this  quantity,  plus 
the  heat  of  dissociation  of  that  part  of  the  acid  or  base 
which  is  undissociated. 

This  explains  the  difference  between  the  amounts  of 
heat  liberated,  when  both  the  acids  and  bases  are  strong, 
and  when  either  the  acid  or  base  is  weak. 

The  theory  of  electrolytic  dissociation  is,  then,  strictly  in 
accord  with  the  facts,  as  far  as  the  heat  of  neutralization  is 
concerned.  This  applies  not  simply  to  the  strong  acids 
and  bases,  but  to  the  apparently  exceptional  cases  of  the 
weakly  dissociated  compounds. 

It  will  be  observed,  that  in  the  above  interpretation  of 
the  process  of  neutralization,  it  is  assumed  that  all  of  the 
hydrogen  and  hydroxyl  ions  combine  to  form  water.  It 
has  been  shown  by  six  separate  lines  of  work,  that  when- 
ever hydrogen  and  hydroxyl  ions  come  together  they 
combine  and  form  water.  This  is  the  same  as  to  say 
that  water  is  undissociated.  The  apparent  assumption  is, 
therefore,  well  supported  by  the  experimental  facts. 

Hess's  Law  of  the  Thermoneutrality  of  Salt  Solutions.  - 
A  dilute  aqueous  solution  of  a  salt  is,  in  terms  of  our  theory, 
a  solution  of  ions.  Thus,  a  dilute  aqueous  solution  of 
potassium  chloride  contains  only  potassium  and  chlorine 
ions.  Similarly,  a  dilute  solution  of  sodium  chloride  is  but 
a  solution  of  sodium  and  chlorine  ions.  When  the  solutions 


EVIDENCE  FOR  THE  THEORY  123 

of  the  two  salts  are  mixed,  the  mixture  contains  only  po- 
tassium, sodium,  and  chlorine  ions. 

'  + 
KC1  in  dilute  aqueous  solution  =  K  +  Cl. 

+ 
NaCl  in  dilute  aqueous  solution  =  Na  -f-  Cl. 

When  the  two  solutions  are  mixed,  we  have :  — 

K  +  Na  +  Cl  +  Cl, 

and  there  should  be  no  thermal  change  produced  on  mix- 
ing such  solutions.  It  has  long  been  known,  that  if  com- 
pletely dissociated  solutions  of  neutral  salts  are  mixed, 
there  is  neither  evolution  nor  absorption  of  heat,  provided 
that  none  of  the  ions  unite  to  form  molecules,  or  to  form 
new  complexes  of  ions.  These  facts  are  usually  stated  as 
Hess's  law  of  the  thermoneutrality  of  salt  solutions,  which 
but  names  them,  without  attempting  an  explanation. 

The  theory  of  electrolytic  dissociation  not  only  furnishes 
a  reason  for  the  law  of  the  thermoneutrality  of  salt  solu- 
tions, but  makes  it  a  necessary  consequence  of  its  own 
validity. 

OSMOTIC     PRESSURE LOWERING     OF     FREEZING-POINT 

RISE   IN    BOILING-POINT  —  CONDUCTIVITY 

It  will  be  remembered  that  Arrhenius  proposes  the 
theory  of  electrolytic  dissociation,  to  account  for  the  abnor- 
mally large  osmotic  pressure  shown  by  certain  classes  of 
substances.  We  may  divide  chemical  compounds  into  two 
classes,  with  respect  to  their  power  to  exert  osmotic  press- 
ure :  First,  substances  like  the  carbohydrates,  alcohols, 
etc.,  i.e.  the  chemically  inactive  organic  compounds,  which 
exert  an  osmotic  pressure  that  obeys  the  gas  laws,  and 


124  ELECTROLYTIC  DISSOCIATION 

will  be  called  normal ;  second,  the  acids,  bases,  and  salts 
which  exert  a  much  greater  osmotic  pressure. 

If  we  determine  the  freezing-point  lowering  produced  by 
these  substances,  when  dissolved  in  water,  we  will  find  that 
they  again  divide  themselves  into  two  classes ;  the  organic 
compounds  giving  freezing-point  lowerings  which  we  will 
call  normal,  and  the  acids,  bases,  and  salts,  giving  a 
greater  depression  of  the  freezing-point.  All  of  those 
compounds,  and  only  those,  which  show  too  great  osmotic 
pressure,  give  too  great  lowerings  of  the  freezing-point  of 
water. 

Furthermore,  if  we  study  the  rise  in  the  boiling-point  of 
solvents  produced  by  dissolved  substances,  we  will  find, 
again,  that  the  organic  compounds  above  referred  to  pro- 
duce a  certain  rise  in  the  boiling-point,  while  all  the  acids, 
bases,  and  salts  produce  a  greater  rise  in  boiling-point. 
Substances  divide  themselves  here,  as  in  the  last  two  cases, 
into  two  classes,  and  it  is  exactly  the  same  division  as 
shown  both  by  osmotic  pressure,  and  lowering  of  freezing- 
point. 

Finally,  if  we  study  the  conductivity  of  solutions  of 
chemical  compounds,  we  will  find  that  solutions  of  the  neu- 
tral organic  compounds  do  not  conduct  the  current,  while 
solutions  of  all  acids,  bases,  and  salts,  do  conduct.  If  we 
were  to  divide  all  chemical  substances  with  respect  to  their 
power  to  conduct  the  electric  current,  they  would  again 
fall  into  two  classes,  and  exactly  the  same  two  classes  as 
were  furnished  by  each  of  the  above  three  properties. 
Substances  which  conduct  the  current  are  termed  electro- 
lytes, and  those  which  do  not  conduct,  non-electrolytes ;  so 
that  we  will  now  refer  to  these  two  classes  of  chemi- 


EVIDENCE   FOR  THE  THEORY  12$ 

cal  compounds  as,  respectively,  electrolytes  and  non- 
electrolytes. 

We  have,  then,  this  very  remarkable  relation.  All  of 
those  substances,  and  only  those,  which  show  abnormally 
great  osmotic  pressure,  show  abnormally  great  lowering  of 
the  freezing-point,  rise  in  boiling-point,  and  conduct  the 
current.  These  electrolytes,  as  we  will  see  later,  are  also 
the  most  active  chemically. 

The  converse  is  also  true,  that  all  of  those  substances, 
and  only  those,  which  show  normal  osmotic  pressures, 
show  normal  lowering  of  freezing-point,  rise  in  boiling- 
point,  and  do  not  conduct  the  current.  These  non-electro- 
lytes, as  we  will  also  see,  are  the  least  active  of  chemical 
substances. 

Having  found  this  qualitative  relation,  it  remains  to  see 
whether  it  is  quantitative,  —  whether  a  substance  which 
shows  too  great  osmotic  pressure  produces  a  lowering  of 
freezing-point,  and  rise  in  boiling-point,  which  is  too  great, 
by  the  same  amount. 

If  the  abnormally  great  osmotic  pressure  is  explained  by 
the  dissociation  of  molecules  into  ions,  so,  also,  must  the 
abnormally  great  lowering  of  freezing-point,  and  rise  in 
boiling-point,  produced  by  electrolytes,  as  well  as  their 
conductivity,  be  due  to  the  same  cause.  If  the  theory  of 
electrolytic  dissociation  is  true,  there  must  be  a  quantitative 
relation  between  abnormal  osmotic  pressure,  lowering  of 
freezing-point,  rise  in  boiling-point,  and  conductivity.  If 
such  a  quantitative  relation  can  be  shown  to  exist,  it 
would  be  a  strong  argument  in  favor  of  the  theory  we 
are  considering.  We  will  show  that  such  a  relation  does 
exist. 


126  ELECTROLYTIC  DISSOCIATION 

Relation  between  Osmotic  Pressure  and  Lowering  of  Freez- 
ing-point. —  The  relations  between  the  four  properties 
here  considered  will  be  pointed  out,  first  experimentally, 
and  then  in  part,  theoretically. 

De  Vries1  has  measured  the  relative  osmotic  pressures 
of  a  number  of  solutions,  using  vegetable  cells.  Without 
going  into  the  details  of  this  method,  the  principle  can  be 
concisely  stated.  When  some  vegetable  cells,  containing 
colored  protoplasm  surrounded  by  a  semipermeable  mem- 
brane, are  immersed  in  solutions  which  have  a  greater 
osmotic  pressure  than  the  contents  of  the  cell,  we  can 
see  the  contents  of  the  cell  contracted  to  one  side,  due  to 
the  loss  of  water  to  the  solution.  If  the  solution  in  which 
the  cell  is  immersed  has  the  same  osmotic  pressure  as  the 
contents  of  the  cell,  no  water  will  pass  into  or  out  of  the 
cell,  and  it  will  present  a  normal  appearance.  If  the  solu- 
tion has  a  smaller  osmotic  pressure  than  the  contents  of 
the  cell,  water  will  pass  in,  and  the  cell  will  be  distended. 
By  studying  the  behavior  of  the  cell  in  the  solution,  under 
the  microscope,  we  can  determine  whether  the  solution  has 
a  greater,  less,  or  the  same  osmotic  pressure  as  the  con- 
tents of  the  cell.  By  starting  with  a  solution  which  has 
a  greater  osmotic  pressure  than  the  contents  of  the  cell, 
and  diluting  it  gradually,  we  can  determine,  from  the 
behavior  of  the  cell,  when  its  osmotic  pressure  is  just  equal 
to  that  of  the  contents  of  the  cell.  We  can  thus  pre- 
pare solutions  of  different  substances,  having  each  the 
same  osmotic  pressure  as  the  cell  contents,  and,  therefore, 
all  having  the  same  osmotic  pressure.  Such  solutions, 
which  have  the  same  osmotic  pressure,  were  termed  isos- 

1  Ztschr.  phys.  Chem.,  2,  415. 


EVIDENCE  FOR  THE  THEORY  127 

motic.  When  these  concentrations  were  expressed  in 
molecular  quantities,  their  reciprocal  values  were  termed 
isotonic  coefficients.  These  show,  directly,  the  relative 
osmotic  pressures  of  solutions  of  equal  molecular  concen- 
tration. The  coefficients  for  a  number  of  compounds,  as 
compared  with  the  molecular  lowerings  of  the  freezing- 
point,  are  given  in  the  following  table,  taken  directly 
from  the  work  of  De  Vries.1 

SUBSTANCE  ISOTONIC  COEFFICIENTS  MOLEC.  Low.  OF  FREEZING- 

MULTIPLIED  BY  100  POINT  MULTIPLIED  BY  IO 

C6H1206  181  185 

C12H22OU  188  193 

MgSO4  196  192 

KNO3  300  308 

K2S04  391  390 

NaCl  305  351 

These  are  just  a  few  of  the  many  cases  given  by  De 
Vries.  But  they  are  sufficient  to  show  the  proportionality 
between  isotonic  coefficients  and  molecular  lowering  of  the 
freezing-point  for  a  number  of  classes  of  substances. 

Relation  between  Osmotic  Pressure  and  Lowering  of 
Vapor-tension.  Rise  in  Boiling-point  —  In  the  same  table 
in  which  the  above  relation  is  pointed  out,  De  Vries  also 
shows  that  a  proportionality  exists  between  the  isotonic 
coefficients  of  a  number  of « substances,  and  the  molecular 
lowering  of  the  vapor-tension;  lowering  of  vapor-tension 
being  used  here,  instead  of  rise  in  boiling-point,  which  is 
proportional  to  it.  A  few  results  taken  from  the  table 
are  given :  — 

1  Ztschr.  phys.  Chem.,  2,  427. 


128 


ELECTROLYTIC  DISSOCIATION 


SUBSTANCE 

C4H605 
C4H606 
NaN03 
K2C204 

K2S04 
CaCl2 
K3C6H507 


IsoTONic  COEFFICIENTS 

MULTIPLIED   BY   IOO 
198 

2O2 
300 

393 
391 
433 
SGI 


LOWERING  OF  VAPOR-TENSION 
MULTIPLIED  BY  IOOO 


I78 

188 
296 
372 


499 


The  proportionality  between  osmotic  pressure  and  low- 
ering of  vapor-tension,  or  rise  in  boiling-point,  is  at  once 
apparent. 

Relation  between  Osmotic  Pressure  and  Conductivity.  — 
De  Vries  also  compared  the  osmotic  pressure  of  solutions 
and  their  conductivity.  He  calculated  the  sum  of  the 
molecules  and  ions,  on  the  one  hand  from  osmotic  press- 
ure, on  the  other  from  conductivity,  and  then  compared 
the  two  values  to  see  how  they  agreed.  He  obtained  the 
following  results : l  — 

SUM  OF  MOLECULES  AND  IONS  CALCULATED  — 
FROM  ISOTONIC  COEFFICIENTS          FROM  CONDUCTIVITY 


SUBSTANCE 
Non-conductors 

C3H803 
C6H1206 


Conductors 

MgS04 

KN08 

KC1 

NaCl 

NH4C1 


IOO 

1 06 

101 


125 

176 

181 
179 
182 
230 


IOO 
IOO 
IOO 

135 
1 80 

187 

182 

185 

234 


Ztschr.  phys.  Chem.,  3,  109;  also  loc.  cit. 


EVIDENCE  FOR  THE  THEORY  I2Q 

The  agreement  between  osmotic  pressure  and  lowering 
of  freezing-point,  rise  in  boiling-point,  and  conductivity,  is 
as  close  as  could  be  expected,  when  we  consider  the  large 
experimental  error  involved  in  determining  osmotic  press- 
ure, directly,  by  any  method,  and  even  in  determining  the 
relative  osmotic  pressure  of  solutions  by  the  method  of 
De  Vries. 

Relation  between  Lowering  of  Freezing-point  and  Rise 
in  Boiling-point.  —  Raoult l  has  shown,  purely  empirically, 
that  the  lowerings  of  the  freezing-point,  produced  by  some 
eighteen  salts,  stand  in  the  same  relation  to  one  another 
as  the  rise  in  boiling-point  produced  by  these  same  com- 
pounds. The  results  are  not  tabulated,  and,  therefore, 
will  not  be  given  here. 

Relation  between  Lowering  of  Freezing-point  and  Con- 
ductivity.— That  a  quantitative  relation  exists  between 
these  quantities,  for  any  given  substance,  was  shown  by 
Arrhenius,  when  he  proposed  the  theory  of  electrolytic 
dissociation.  Some  of  the  data  which  he  brought  forward 
to  prove  this  point  have  already  been  given  (p.  98).  The 
agreement  between  the  values  of  z,  as  calculated  from  freez- 
ing-point lowering  and  from  conductivity,  was  only  fairly 
close,  because  the  freezing-point  method  at  that  time  was 
in  a  crude  state,  and  gave  only  approximate  results. 

The  freezing-point  method  has  now  been  greatly  im- 
proved,2—  a  number  of  sources  of  error  having  been  elimi- 
nated, —  until  it  can  be  used  to  measure  the  value  of  the 
coefficient  of  dissociation,  as  it  is  termed,  with  considerable 


1  Compt.  rend.,  70,  1349  (1870). 

2  Jones,  Ztschr.  phys.  Chem.,  n,  no  and  529;  12,  623.    Loomis,  Wied.  Ann., 
51,  500;  57,  495  ;  60,  523.     Raoult,  Ztschr.  phys.  Chem.,  27,  617. 


1 3o 


ELECTROLYTIC   DISSOCIATION 


accuracy.  The  values  of  a  have  been  determined  by  Jones,1 
for  a  large  number  of  dilutions  of  different  substances, 
using  the  freezing-point  method.  These  have  been  com- 
pared with  the  values  of  «  for  the  same  dilutions  of  the 
same  substances,  using  the  conductivity  method.  The  fol- 
lowing results  are  taken  from  the  paper  of  Jones :  — 

a  FROM  a  FROM  FREEZING- 

POINT  LOWERING 

98.4 

90.5 
84.1 

94.2 
87.6 

77-7 
98.4 
95-8 
88.6 

86.0 
83-8 
60.7 

98.4 
93-7 
83.1 

96.6 
96.0 
77-5 

The  percentage  of  dissociation  a,  as  measured  by  the 
freezing-point  method,  agrees  surprisingly  well  with  the 
values  obtained  from  conductivity.  The  slight  differences 
which  exist  are  probably  due  to  the  different  temperatures 

l  Phil.  Mag.,  36,  483. 


COMPOUNDS 

CONCENTRATION 

CONDUCTIVI 

NaCl 

O.OOI 

98.0 

NaCl 

0.0  1 

93-5 

NaCl 

O.I 

84.1 

BaCl2 

O.OOI 

93-9 

BaCl2 

0.005 

87.9 

BaCl2 

0.05 

75-3 

HC1 

O.OO2 

IOO.O 

HC1 

O.OI 

98.9 

HC1 

O.I 

93-9 

H2S04 

0.003 

89.8 

H2S04 

0.005 

854 

H2S04 

0.05 

62.3 

KOH 

0.002 

IOO.O 

KOH 

O.OI 

99.2 

KOH 

O.I 

92.8 

K2C03 

0.003 

92.0 

K2C03 

0.005 

88.6 

K2C03 

0.05 

71.9 

EVIDENCE   FOR  THE  THEORY  131 

at  which  the  two  sets  of  measurements  were  made  —  con- 
ductivity being  determined  at  18°,  and  freezing-point 
lowering  a  little  below  o°. 

We  have  now  demonstrated,  by  experiment,  the  quan- 
titative relation  which  exists  between  osmotic  pressure, 
lowering  of  freezing-point,  rise  in  boiling-point,  and  con- 
ductivity. We  will  now  give  a  mathematical  demonstration 
of  one  or  two  of  these  relations. 

Connection  between  Osmotic  Pressure  and  Lowering  of 
Freezing-point,  established  by  Thermodynamics.  —  The  con- 
nection between  osmotic  pressure  and  lowering  of  the 
freezing-point  was  deduced  thermodynamically  by  van't 
Hoff,1  in  the  paper  to  which  reference  has  so  often  been 
made. 

Van't  Hoff  showed  that  solutions  in  the  same  solvent, 
having  the  same  freezing-point,  are  isotonic  at  that  tem- 
perature. He  applied  this  to  dilute  solutions,  and  was  led 
to  the  conclusion  that  solutions  which  contain  the  same 
number  of  molecules  in  the  same  volume,  and,  therefore, 
from  Avogadro's  law,  are  isotonic,  have  also  the  same 
freezing-point.  This  was  discovered  experimentally  by 
Raoult,  and  led  to  the  expression  "  normal  molecular  lower- 
ing of  the  freezing-point."  This  means  the  lowering  in 
degrees,  produced  by  a  gram-molecular  weight  of  the  sub- 
stance in  100  grams  of  the  solvent.  This  normal  molecular 
lowering  of  the  freezing-point,  which  we  will  term  the 
freezing-point  constant  for  the  solvent,  van't  Hoff  then 
derived  from  the  latent  heat  of  fusion  of  the  solvent. 
This  deduction  has  been  developed  more  fully  by  Ostwald,2 

1  Harper's  Science  Series,  IV,  29.    Ztschr.  phys.  Chem.  I,  481. 

2  Lehrb.  allg.  Chem.,  I,  p.  759. 


132  ELECTROLYTIC   DISSOCIATION 

and  it  will  be  given  here  essentially  as  worked  out  by  him, 
with  some  changes  1  which  seem  to  make  the  steps  a  little 
clearer. 

Let  us  take  a  solution  consisting  of  n  gram-molecules  of 
the  dissolved  substance  and  N  gram-molecules  of  the  sol- 
vent. Let  T  be  the  temperature  of  solidification  of  the 
solvent,  and  A  the  lowering  of  the  freezing-point.  Here 
as  much  of  the  solvent  is  allowed  to  solidify  as  would 
serve  for  the  solution  of  one  gram-molecule  of  the  sub- 

tance,  =—  molecules. 
n 

Let  X  be  the  latent  heat  of  fusion  of  a  gram-molecule  of 

N 

the  solvent  ;  the  amount  of  heat  liberated  would  be  —  X.   If, 

n 

now,  the  ice  is  separated  from  the  solution,  warmed  to  tem- 
perature T,  and  melted,  and  finally  allowed  to  mix  with  the 
solution  by  passing  through  a  semipermeable  membrane,  it 
will  exert  an  osmotic  pressure  /.  If  v  is  the  volume  of  the 

solvent  which  solidified,  the  work  =/?>,  the  heat  —X;  from 
which:- 


N\      T 
But  pv  —  R  T,  and  R  =  2  cal.     Substituting,  we  have  :  — 


N   X 

Let  M  be  the  molecular  weight  of  the  solvent,  and  sub- 
stituting N  —  -jr,  we  have  :  — 


100    X 

1  Jones,  Phil.  Mag.,  36,  493. 


EVIDENCE   FOR  THE  THEORY  133 

x* 

In  the  Raoult  formula  m  =  —:tm  is  the  molecular  weight 

A 

of  the  dissolved  substance,  K  is  the  freezing-point  constant, 
and  A  the  specific  lowering  of  the  freezing-point.     A  =—  , 

where  A  is  the  lowering  of  the  freezing-point  observed,  and 
/  the  percentage  concentration  of  the  solution. 


-. 

Let  n  be  the  number  of  molecules  of  the  dissolved  sub- 
stance in  100  g.  of  the  solvent. 


substituting,  wA  =  Kmn  ; 

A  =  ^«  ........    (2) 

M    i  T* 

From  (i)  and  (2)          K=—  ~^. 

100     \ 

If  L  is  the  heat  of  fusion  of  i  g.  of  the  solvent, 


Substituting,  K  = 

From  this  equation  van't  Hoff  has  calculated  th'e  value 
of  the  freezing-point  constant  for  a  number  of  solvents, 
and  compared  these  values  with  those  found  experimentally. 

CONSTANT  CALCULATED  CONSTANT  FOUND 

FROM  K=  — —  EXPERIMENTALLY 

TOO  L 

Water  18.9  18.5 

Acetic  acid  38.8  38.6 

Formic  acid  28.4  27.7 

Benzene  53.0  50.0 

Nitrobenzene  69.5  70.7 


134 


ELECTROLYTIC  DISSOCIATION 


The  values  of  the  freezing-point  constant,  as  calculated 
from  the  van't  Hoff  formula,  agree  very  satisfactorily  with 
those  found  by  experiment. 

Relation  between  Osmotic  Pressure  and  Lowering  of 
Vapor-tension  (Rise  in  Boiling-point).  Theoretical  Demon- 
stration. —  The  relation  between  osmotic  pressure  and 
lowering  of  vapor-pressure  has  been  derived  in  a  simple 
manner  by  Arrhenius.1  The  line  of  reasoning  is  as  fol- 
lows :  Given  a  vessel  of  the  form  shown  in  Fig.  5, 
closed  at  the  bottom  by  a  semiperme- 
able  wall.  Let  this  vessel  be  filled  with 
a  solution  S,  and  dip  into  a  vessel  con- 
taining the  pure  solvent  D.  The  whole 
is  covered  with  a  bell-jar,  and  exhausted. 
Equilibrium  will  be  established  when  the 
pressure  of  the  column  of  liquid,  from 
the  surface  of  the  solvent  up  to  h,  is 
.  equal  to  the  osmotic  pressure,  and  the 
free  space  is  saturated  by  the  vapor 
D1.  When  equilibrium  is  established, 
the  vapor-pressure  of  the  solution  at 
h  must  be  just  equal  to  the  pressure 
of  the  vapor  of  the  solvent  at  this  point. 
If  it  were  less,  liquid  would  condense  in  k,  if  more,  it 
would  distil  out  of  h,  and  there  would  not  be  equilibrium, 
since  liquid  would  flow  either  out  or  in  through  the  mem- 
brane. If  /'  is  the  tension  of  the  vapor  of  the  solution  at 
h,  f  the  vapor-tension  of  the  solvent,  h  the  height  of  the 
column  of  liquid,  and  d  the  density  of  the  vapor  in  the 
bell-jar,  we  have  :  -  yv  =y  _  hd 

1  Ztschr.  phys.  Chem.,  3,  115. 


FIG.  5. 


EVIDENCE   FOR  THE  THEORY  135 

The  value  of  h.  —  Let  us  have  a  very  dilute  solution,  in 
which  n  gram-molecules  of  substance  are  contained  in 
g  grams  of  solvent.  From  van't  HofFs  law  of  osmotic 
pressure  we  would  have  :  — 


in  which  P  is  the  osmotic  pressure  of  the  solution,  and  V 
its  volume.  Let  s  be  the  specific  gravity  of  both  solution 
and  solvent  ;  they  are  practically  the  same  for  very  dilute 
solutions. 


Substituting,        P  V=  nR  T  =        =  hg  ; 
hg=nRT  .\  k  = 


s 

nRT 


The  value  of  d.  —  Let  v  be  the  volume  of  a  gram- 
molecule  of  the  vapor  of  the  solvent  D,  and  /the  pressure 
of  this  vapor  :  — 


RT 


If  M  is  the  molecular  weight  of  the  solvent 


d       f  RT 


136  ELECTROLYTIC  DISSOCIATION 


Substituting   the   values,    /fc  =      -and  ^  =       ,in  the 

g  Kl 

equation  /'=/—  hd,  we  have:  — 


f.f-lM, 

g 


or, 


which  is  essentially  Raoult's  fundamental  equation  for  the 
lowering  of  the  vapor-pressure  of  a  solvent  by  a  dissolved 
substance.  Raoult's  equation,  which  has  been  amply  veri- 
fied by  experiment,  is  usually  written  :  — 


/       -N 

where  N  is  the  number  of  gram-molecules  of  the  solvent. 
It  is  evident  that  N=^-  when  the  two  equations  become 
identical.  M 

Theoretical  demonstrations  of  other  relations  between 
the  four  properties  of  solutions,  which  we  are  considering, 
have  been  furnished.  Thus,  Guldberg  *  has  proved  a  direct 
connection  between  lowering  of  freezing-point  and  lower- 
ing of  vapor-tension.  Arrhenius  2  has  shown  how  freezing- 
point  lowering  and  conductivity  are  connected,  by  cal- 
culating the  value  of  the  coefficient  i  from  both,  and  then 
showed,  experimentally,  that  the  two  values  agreed  with 

1  Compt.  rend.,  70,  1349.  2  Loc.  cit. 


EVIDENCE  FOR  THE  THEORY  137 

one  another  (see  p.  98).  A  number  of  other  demonstra- 
tions of  relations  between  these  properties  could  be  given, 
did  space  permit,  but  quite  enough  has  been  developed  to 
show,  both  experimentally  and  theoretically,  that  they  are 
quantitatively  connected.  Whatever  causes  electrolytes  to 
exert  a  greater  osmotic  pressure  than  non-electrolytes,  also 
causes  them  to  produce  a  greater  lowering  of  the  freezing- 
point,  rise  of  boiling-point,  and  enables  them  to  conduct 
the  current. 

Arrhenius  showed  that  his  theory  explains  all  of  the 
facts  concerning  osmotic  pressure.  From  the  above  rela- 
tions alone  it  must,  therefore,  accord  with  the  facts  con- 
nected with  the  other  three  properties.  We  have,  however, 
an  abundance  of  independent  evidence,  were  this  neces- 
sary, that  the  theory  of  electrolytic  dissociation  is  in  per- 
fect harmony,  not  only  with  what  is  known  of  the  osmotic 
pressure  of  dilute  solutions,  but  with  every  other  property 
possessed  by  them. 

EXPERIMENT   TO    SHOW   THE    PRESENCE    OF    FREE    IONS 

If  only  ions  conduct,  then,  whenever  a  current  is  passed 
through  a  solution  of  an  electrolyte,  a  movement  of  the 
ions  is  necessarily  involved.  The  same  applies  to  a 
solution  of  an  electrolyte  charged  electrostatically.  If 
the  charging  body  is  negative,  it  will  attract  the  ions 
which  carry  the  positive  electricity  in  the  solution,  i.e. 
the  cations,  and  will  repel  the  anions.  If  the  solution 
could  then  be  separated  into  two  parts,  the  one  would 
contain  an  excess  of  cations,  and  the  other  an  excess  of 
anions. 


138  ELECTROLYTIC  DISSOCIATION 

Illustration  of  a  Solution  charged  Electrostatically.  — 
Let  two  vessels,  A  and  B,  be  filled  with  a  solution  of  an 

electrolyte,  say  potassium 
chloride,  and  let  the  two 

K   ~  A  £f  1}  B 

^ —  —      be   connected  with    a    SI- 


FIG.  6.  *—^>  phon  filled  with  the  same 

liquid.  Let  a  negatively 

charged  body  K  be  brought  near  to  A ;  it  will  act  by  in- 
duction upon  the  system  AHB.  A  will  become  positive 
and  B  negative.  If  now  the  siphon  H  is  removed,  and 
then  the  body  K,  A  will  remain  positive  and  B  negative. 

But,  from  the  law  of  Faraday,  electricity  can  move  in 
solutions  only  by  a  movement  of  the  ions.  That  A  should 
be  positive,  it  is  necessary  that  it  should  contain  an  excess 
of  the  potassium  ions  which  carry  the  positive  charge. 
Similarly,  B  must  contain  an  excess  of  chlorine  ions.  The 
number  of  these  free  ions  in  the  solution  must  depend, 
of  course,  upon  the  intensity  of  the  inducing  action.  To 
discharge  A,  introduce  a  platinum  wire  connected  with  the 
earth.  The  potassium  ions  give  up  their  positive  charge 
to  the  wire,  and  become  atoms.  These  now  act  upon  the 
water,  forming  potassium  hydroxide,  and  hydrogen  which 
escapes  from  the  solution. 

This  experiment  was  proposed  by  Ostwald,1  simply  as 
an  illustration.  It  is  obvious  to  any  one  that,  under  condi- 
tions such  as  those  described,  the  amount  of  hydrogen  set 
free  would  be  far  too  small  to  be  seen.  On  account  of  the 
very  great  charge  carried  by  an  ion,  the  number  of  ions 
which  would  be  induced  from  one  vessel  to  the  other,  by 
the  above  arrangement,  would  be  relatively  small. 

1  Zlschr.  phys.  Chem.,  2,  272. 


EVIDENCE  FOR  THE  THEORY  139 

The  al>ove  experiment  illustrates  another  point,  as 
Ostwald  has  shown.  That  electrostatic  charging  of  elec- 
trolytes takes  place  with  enormous  velocity,  as  with  con- 
ductors of  the  first  class.  But  Kohlrausch  has  shown 
that  the  ions  move  very  slowly.  If  the  above  induction 
phenomenon  takes  place  very  rapidly  in  the  solution,  then 
the  potassium  ion,  which  brings  the  positive  charge  closest 
to  K,  could  not  have  been  connected  with  the  chlorine 
ion,  which  takes  the  negative  charge  to  the  region  most 
remote  from  K.  Free  ions  must,  therefore,  be  present 
in  the  solution  at  all  times,  or  the  electrolyte  must  be 
dissociated. 

Experiment  of  Ostwald  and  Nernst.  —  The  experiment 
described  above,  while  theoretically  correct,  must  be  re- 
garded as  only  an  illustration.  Ostwald  and  Nernst * 
have,  however,  devised  an  experiment,  which  they  claim 
demonstrates  to  the  eye  the  effect  described  by  Ostwald. 
To  be  able  to  see  the  hydrogen  liberated  by  induction, 
unusual  precautions  must  be  taken,  because  of  the  very 
small  quantity  of  gas  which  will  be  set  free.  To  liberate 
a  milligram  of  hydrogen  would  require  a  condenser  of 
about  one  square  kilometre.  But  one  milligram  of  hydro- 
gen will  fill  12  to  13  cubic  centimetres,  under  ordinary 
conditions. 

By  means  of  a  microscope,  it  is  possible  to  see  a  bub- 
ble of  gas  o.oi  mm.  in  diameter,  and  this  amount  could 
be  liberated,  using  a  condenser  of  ordinary  dimensions. 
The  gas  was  collected  in  the  capillary  of  a  Lippmann 
electrometer,  since  a  small  quantity  could  be  easily  recog- 
nized in  this  way. 

1  Ztschr.  phys.  Chem.,  3,  271  (1888). 


140  ELECTROLYTIC   DISSOCIATION 

The  experiment  of  Ostwald  and  Nernst  will  now  be 
described  in  detail. 

A  glass  tube  30  to  40  cm.  in  length,  provided  with  a 
stop-cock,  was  drawn  out  at  one  end  to  a  fine  capillary. 
The  diameter  of  the  capillary  was  such  that,  when  the 
tube  was  filled  with  mercury,  it  would  begin  to  flow  out  of 
the  fine  point.  The  tube  was  fastened  upright,  and  its 
tip  allowed  to  dip  in  dilute  sulphuric  acid.  The  mercury 
was  then  drawn  up  into  the  capillary,  and  the  acid  drawn 
in  after  it.  By  means  of  the  stop-cock,  the  surface  of 
contact  between  the  mercury  and  the  acid  could  be  kept 
about  the  middle  of  the  capillary.  A  platinum  wire, 
fused  into  the  glass  tube,  connected  with  the  mercury. 

A  large  glass  flask  was  filled  with  dilute  sulphuric  acid. 
Its  outer  surface  was  covered  with  tinfoil,  and  its  neck 
varnished  with  shellac.  The  contents  of  the  flask  were 
connected  with  the  sulphuric  acid  into  which  the  capillary 
tube  dipped,  by  means  of  a  moist  cord.  The  glass  flask 
was  insulated,  by  placing  it  upon  a  plate  of  hard  rubber. 
The  outer  coating  on  the  flask  was  connected  with  the  pos- 
itive pole  of  a  small  machine  for  generating  electricity ;  the 
mercury  in  the  tube  connected  with  the  earth.  When  the 
machine  was  set  in  motion,  the  meniscus  in  the  capillary 
rushed  up  with  violence,  and  at  the  same  time,  several 
bubbles  of  gas  separated,  which  broke  the  thread  of  mer- 
cury in  a  number  of  places.  This  is  nearly  the  verbatim 
account  of  what  happened,  as  given  by  the  experimenters 
themselves. 

They  explain  the  facts  as  follows:  "By  charging  the 
coating  on  the  'outside  of  the  flask  with  positive  electricity, 
the  negative  electricity  in  the  interior  is  attracted  and  held, 


EVIDENCE  FOR  THE  THEORY  141 

while  the  positive  is  repelled.  The  latter  passes  through 
the  thread,  into  the  capillary  electrode,  and  through  the 
platinum  wire  in  the  latter  to  the  earth.  There  is  no 
closed  current  present ;  the  entire  movement  of  electricity 
which  is  produced  is  the  result  of  induction." 1 

As  the  outer  coating  of  the  flask  becomes  charged  with 
positive  electricity,  the  ions  SO4,  which  carry  the  nega- 
tive charge,  are  attracted,  the  positive  ions,  hydrogen,  are 
repelled,  pass  over  the  moist  cord  to  the  mercury,  give  up 
their  charge,  and  appear  as  ordinary  hydrogen  gas. 

The  objection  could  be  raised  to  this  experiment,  that 
a  movement  of  electricity  takes  place,  electrolytically, 
through  the  glass,  and  that  this  causes  the  separation  of 
the  hydrogen.  The  authors  performed  a  number  of  ex- 
periments to  test  this  point,  and  convinced  themselves 
that  this  is  strictly  an  induction  phenomenon. 

They  worked  quantitatively,  as  far  as  possible,  determin- 
ing^  the  amount  of  hydrogen  which  separates  and  the 
amount  of  the  electricity  induced,  and  found  that  the 
amount  of  gas  liberated  corresponded  to  that  calculated 
from  Faraday's  law  to  within  the  limit  of  experimental 
error.  They  concluded  that  movement  of  electricity  in 
electrolytes,  corresponding  to  Faraday's  law,  can  take 
place  only  with  a  simultaneous  movement  of  the  ions,  and 
that  in  electrostatically  charged  electrolytes  a  number  of 
ions,  corresponding  to  the  amount  of  electricity,  are  free. 

The  question  still  remains,  whether  the  ions  are  not  set 
free  at  the  moment  of  the  electrostatic  charging,  so  that 
the  separation  of  the  electricities  is  accompanied  by  a  kind 
of  electrolysis  in  the  interior  of  the 'liquid.  Ostwald  and 

l  Ztschr.  phys.  Chem.,  3,  122. 


142  ELECTROLYTIC  DISSOCIATION 

Nernst  point  out,  that  Clausius1  has  shown,  that  the 
movement  of  electricity  in  electrolytes  obeys  the  weakest 
electromotive  impulses,  which  would  not  be  possible  if 
the  electricity  must  first  perform  an  appreciable  amount 
of  work.  They  then  show  that  such  an  assumption  is 
against  the  laws  of  thermodynamics. 

If  we  consider  all  of  the  precautions  which  Ostwald  and 
Nernst  have  taken,  it  seems  that  they  have  conclusively 
proved  the  point,  that  free  ions  exist  in  electrostatically 
charged  electrolytes,  and  these  are  not  set  free  at  the 
moment  of  charging. 

THE   OSTWALD    DILUTION   LAW 

Conductivity  and  Dilution.  —It  is  well  known,  that  the 
power  of  solutions  of  electrolytes  to  conduct  the  current 
increases  with  the  dilution.  If  we  always  deal  with 
molecular  quantities,  and  express  the  conducting  power 
of  solutions  in  terms  of  molecular  conductivity,  we  will 
see  at  a  glance,  that  this  is  always  larger  (with  a  very  few 
exceptions)  2  the  greater  the  dilution.  The  rate  of  increase 
with  the  dilution  is  comparatively  slow  for  the  good  con- 
ductors, but  much  more  rapid  for  the  poorer  conducting 
substances,  such  as  the  organic  acids.  The  difference 
between  the  molecular  conductivities  of  the  good  and  poor 
conductors  thus  becomes  less  as  the  dilution  increases. 
This  agrees  with  the  view  of  Arrhenius,  that  the  strength 
of  all  acids  which,  as  we  shall  see  later,  depends  only  upon 
the  number  of  hydrogen  ions  present,  is  the  same  at  infi- 
nite dilution,  since  at  this  dilution  all  acids  are  completely 
dissociated. 

1  Pogg.  Ann.,  ioi,  338.  *  Kablukoff,  Ztschr.  phys.  Chem.,  4,  429. 


EVIDENCE  FOR  THE  THEORY  143 

Ostwald  :  found  from  his  own  work,  that  the  molecular 
conductivity  of  all  monobasic  acids  passes  through  the 
same  series  of  values,  and  if  acids  A  and  B  have  the  same 
conductivities  at  dilutions  v  and  vlt  they  will  have  the  same 
conductivities  at  av  and  av^. 

Having  found  such  a  general  relation  between  the  con- 
ductivities of  solutions  of  different  substances,  it  remains 
to  discover  the  mathematical  expression  connecting  dilu- 
tion and  conductivity.  And  since  dissociation  and  con- 
ductivity are  proportional,  we  would  then  have  connected 
dilution  and  dissociation. 

Ostwald's  Deduction  --  Ostwald  2  has  pointed  out,  that 
since  the  laws  of  gas  pressure  apply  to  the  osmotic  press- 
ure of  dilute  solutions  of  non-electrolytes,  if  Arrhenius's 
theory  of  electrolytic  dissociation  to  account  for  the  excep- 
tions shown  by  electrolytes  is  true,  we  ought  to  be  able 
to  apply  the  formula  for  a  partly  dissociated  gas  to  a  partly 
dissociated  solution.3 

For  the  homogeneous  system  of  one  volume  of  a  gas 
dissociating  into  two  volumes  of  gaseous  products,  Ost- 
wald 4  deduced  the  formula  :  — 

^  log  -4r  =  |,+  const. 


p,  /!,  and  /2  are  the  pressures  of  the  original  gas  and  of 
the  decomposition  products,  respectively,  q  is  the  heat  of 
decomposition,  R  is  the  gas  constant,  and  T  the  abso- 
lute temperature. 

1  Journ.  prakt.  Chem.,  31,  433  ;  Lehrb.  allg.  Chem.,  II,  p.  653. 

2  Ztschr.  phys.  Chem.,  2,  136,  276;  3,  170. 
»  See  also  Planck,  Wied.  Ann.,  34,  147. 

4  Ztschr.  phys.  Chem.,  2,  36;  Lehrb.  allg.  Chem.,  II,  p.  723  (ist  edition). 


144  ELECTROLYTIC  DISSOCIATION 

If  the  temperature  is  constant,  and  neither  of  the  de- 
composition products  is  present  in  excess,  the  above 
expression  becomes  :  — 

-2-  =  constant   .     .    .  .    (i) 

P\ 

in  which  /  is  the  pressure  of  the  original  gas,  and  /x 
that  of  the  decomposition  products. 

Turning  now  to  solutions,  we  must  deal  with  osmotic 
pressure  instead  of  gas  pressure.  The  osmotic  pressure 
is  proportional  to  the  amount  of  substance  present,  and 
inversely  proportional  to  the  volume.  Let  u  be  the  mass 
of  the  undecomposed  electrolyte,  and  u^  the  mass  of  the 
decomposition  products;  v  is  the  volume:  — 

/  =  -,  and  /,  =  —  • 

v  ^1      v 

Substituting  these  values  in  (i),  we  have:  — 

uv 

—  -  =  constant  .......     (2) 

u* 

The  amount  of  the  dissociation  products  u^  is  equal  to 
the  relation  between  the  conductivity  at  volume  v  (pv), 
and  the  conductivity  at  infinite  dilution  (p^):  — 

ft 

*?5 

The   amount   of   the    undissociated    substance  u  is   the 
complement  of  u-,:  — 


Substituting  these  values  of  u  and  u^  in  (2)  we  have  :  — 

.    ...    (3) 


EVIDENCE  FOR  THE  THEORY  145 

and  this  is  the  dilution  law  of  Ostwald.  This  can,  how- 
ever, be  simplified.  If  we  represent  the  activity  co- 
efficient, or  the  amount  of  dissociation,  by  a :  — 


Substituting  this  value  in  (3)  and  taking  the  reciprocal, 
we  have: — 

- — ^— —  =  constant (4) 

(i  —  a)v 

Ostwald1  proceeded  at  once  to  test  his  formula  by 
experiment.  The  conductivity  of  a  number  of  acids  at 
different  dilutions  was  measured,  and  the  values  of  a 
calculated  for  these  dilutions.  These  values  of  «,  to- 
gether with  the  volumes  of  the  different  solutions  v, 
(volume  is  the  number  of  litres  which  contains  a  gram- 
molecular  weight  of  the  electrolyte),  were  inserted  in 
equation  (4),  to  ascertain  whether  c  came  out  a  constant, 
over  a  fairly  wide  range  of  concentration. 


v 

8 

16 

32 

64 

128 

256 

512 

1024 


ACETIC  ACED 

a 

c 

1.193 

O.OOlSo 

1.673 

0.00179 

2.38 

0.00182 

3-33 

0.00179 

4.68 

0.00179 

6.56 

O.OOlSo 

9.14 

O.OOlSo 

12.66 

0.00177 

1  Ztschr.  phys.  Chem.,  3,  170, 

241,  369. 

146  ELECTROLYTIC  DISSOCIATION 

O-AMIDOBENZOIC   ACID 

v  a                                           c 

64  2.03  0.00066 

128  3-02  0.00074 

256  4.54  0.00084 

512  6.62  0.00092 

IO24  9.44  0.00096 

The  values  obtained  for  c,  for  most  of  the  acids  in- 
vestigated, approached  a  constant.  Ostwald  studied  be- 
tween two  and  three  hundred  organic  acids,  and  while 
there  are  a  number  of  cases  where  c  did  not  come  out 
very  constant,  yet  it  can  be  said,  in  general,  that  the  law 
holds  approximately  for  this  class  of  substances.  It 
should  be  said,  that  the  organic  acids  are  weakly  dis- 
sociated compounds. 

Bredig,1  in  studying  the  conductivity  of  ammonia,  the 
amines,  and  other  weakly  dissociated  bases,  applied  the 
Ostwald  formula  to  somewhat  more  than  thirty  of  these 
compounds. 

AMMONIA  TRIPHENYLMETHANE  PIPERIDINE 

V  C  V  C  V  C 

8  0.0023  8  0.0069  8  0.157 

32  0.0023  32  0.0075  32  0.162 

64  0.0023  64  0.0076  64  0.150 

256  0.0024  256  0.0074  256  0.152 

The  values  of  c  (for  each  compound)  are  more  nearly 
constant  in  the  work  of  Bredig  on  the  weak  bases,  than 
in  that  of  Ostwald  on  the  weak  acids. 

J  Ztschr.  phys.  Chem.,  13,  289. 


EVIDENCE   FOR  THE  THEORY  147 

While  the  dilution  law  of  Ostwald  holds  fairly  well  for 
the  weakly  dissociated  acids  and  bases,  it  does  not  apply 
at  all  satisfactorily  to  the  strongly  dissociated  electrolytes 
—  the  strong  acids  and  bases,  and  salts  of  these  acids 
and  bases.  The  reason  for  this  failure  on  the  part  of 
Ostwald'  s  law  is  yet  to  be  discovered. 

Rudolph!'  s  Dilution  Law.  —  Rudolphi,1  from  a  study  of 
the  conductivity  of  solutions  of  silver  nitrate  of  varying 
concentrations,  discovered  a  new  relation,  which  obtains 
for  the  strongly  dissociated  compounds.  If  we  represent 
the  volume  by  v,  and  the  constant  by  c,  as  above,  he  found 
that  when  he  applied  the  Ostwald  equation  to  solutions  of 
silver  nitrate,  he  obtained  the  following  values  :  — 

For  v=  1  6,  c  =  0.26. 
For  v  =  64,  £  =  0.13. 
For  v  —  256,  c  —  0.065. 

A  glance  at  these  figures  will  show  that  a  real  constant 
would  be  obtained,  if  the  values  of  c  were  multiplied  by 
the  square  root  of  v  in  each  case  ;  thus  :  — 

0.26  x  Vl6  =  0.13  x  V64  =  0.065 


We  must,  then,  substitute  for  v,  in  the  Ostwald  expres- 
sion, the  square  root  of  v,  when  it  becomes:  — 

-  -  —^  —  -  =  constant. 
(i  -<*)Vtf 

Rudolphi  applied  his  equation  to  between  fifty  and 
sixty  strongly  dissociated  compounds,  and  the  values 
found  for  c  approached  a  constant.  While  marked  devia- 

1  Ztschr.  phys.  Chem.,  17,  385. 


148  ELECTROLYTIC   DISSOCIATION 

tions  are  not  wanting,  yet  Rudolphi's  expression  applies 
as  well  to  the  strongly  dissociated  electrolytes,  as  that  of 
Ostwald  to  those  which  are  less  strongly  dissociated,  as 
the  organic  acids  and  bases.  This  will  be  seen  from  the 
following  examples:  — 

HYDROCHLORIC  ACID  POTASSIUM  SULPHITE  POTASSIUM  ACETATE 


V 

c 

V 

c 

V 

c 

2 

4.36 

2 

0.453 

2 

1.24 

4 

4.45 

8 

0.454 

IOO 

1.19 

8 

5-13 

32 

0.455 

1,000 

1.18 

16 

5-13 

128 

0.544 

10,000 

1.03 

The  Rudolphi  expression  is,  of  course,  purely  empirical. 
The  physical  significance  of  the  V^  is  thus  far  entirely 
unexplained.  One  or  two  modifications 1  of  the  Rudolphi 
formula  have  been  proposed,  but  these  are  also  empirical, 
and  cannot  be  regarded  as  essentially  in  advance  of  the 
original. 

We  thus  have  two  expressions  for  the  relation  between 
the  dissociation  of  electrolytes  and  the  dilution  of  the 
solution :  That  of  Ostwald,  which  has  a  mathematical 
basis,  and  whose  physical  significance  is  known,  apply- 
ing to  the  weakly  dissociated  electrolytes ;  and  that  of 
Rudolphi,.  which  is  purely  empirical,  and  whose  physical 
meaning  is  unknown,  applying  to  the  strongly  dissociated 
electrolytes.  The  relation  between  gaseous  and  electrolytic 
dissociation  is  thus  established,  as  far  as  the  less  strongly 
dissociated  electrolytes  are  concerned ;  but  when  the  dis- 
sociation is  nearly  complete  at  moderate  dilutions,  there 
exists  a  discrepancy  which  still  remains  to  be  explained. 

1  Van't  Hoff,  Ztschr.  phys.  Chem.,  18,  300;  Kohlrausch,  ibid.,  18,  662. 


EVIDENCE  FOR  THE  THEORY  149 

EFFECT   OF   AN    EXCESS   OF    ONE    OF   THE   PRODUCTS    OF 
DISSOCIATION 

Further  Relation  between  Dissociation  by  Heat  and  Elec- 
trolytic Dissociation.  —  It  is  well  known  that  the  dissocia- 
tion of  a  vapor  by  heat  is  diminished  by  the  presence  of 
an  excess  of  any  of  the  products  of  dissociation.  Thus, 
the  vapor  of  ammonium  chloride  is  more  stable  in  the 
presence  of  an  excess  of  ammonia,  or  of  hydrochloric 
acid.  And  the  vapor-density  of  phosphorus  pentachlo- 
ride,  which  breaks  down  by  heat  into  phosphorus  trichlo- 
ride and  chlorine,  when  determined  in  an  atmosphere  of 
chlorine,  agrees  very  nearly  with  the  theoretical  density. 
Many  such  examples  have  been  brought  to  light  by  the 
work  of  Deville  and  others. 

It  would  be  an  interesting  analogy,  if  we  could  find  a 
similar  effect  in  the  case  of  electrolytic  dissociation. 

It  has  long  been  known,  that  when  a  saturated  solution 
of  sodium  chloride  is  treated  with  gaseous  hydrochloric 
acid,  the  gas  dissolves  and  sodium  chloride  separates.  A 
saturated  solution  of  the  salt  contains  sodium  chloride 
molecules,  sodium  ions,  and  chlorine  ions.  When  gaseous 
hydrochloric  acid  dissolves  in  the  solution,  it  dissociates 
into  hydrogen  ions  and  chlorine  ions.  We  have  thus 
added  one  of  the  products  of  dissociation  of  the  original 
compound,  —  chlorine  ions.  The  dissociation  of  the  so- 
dium chloride  is  diminished,  which  is  shown  by  the  fact 
that  some  of  the  ions  combine  to  form  molecules,  and 
these  are  precipitated  from  the  solution. 

The  same  relation  is  shown  by  Nernst 1  in  the  case  of 

1  Ztschr.  phys.  Chem.,  4,  375. 


150  ELECTROLYTIC  DISSOCIATION 

potassium  chlorate.  If  to  a  saturated  solution  of  potas- 
sium chlorate,  either  potassium  or  C1O3  ions  are  added, 
some  of  the  potassium  chlorate  will  be  precipitated. 
Thus,  if  to  a  saturated  solution  of  potassium  chlorate, 
either  potassium  chloride  or  potassium  hydroxide  is 
added,  there  will  soon  result  a  precipitation  of  potassium 
chlorate.  If,  on  the  other  hand,  sodium  chlorate  is  added 
to  a  saturated  solution  of  potassium  chlorate,  some  of  the 
potassium  chlorate  will  be  precipitated.  This  is  at  least 
qualitatively  analogous  to  what  takes  place  in  the  dissocia- 
tion of  a  vapor  by  heat.  It  remains  to  study  this  effect 
quantitatively. 

The  theory  of  the  mutual  effect  of  salts  on  each  other's 
solubility  was  developed  by  Nernst,1  from  the  theory  of 
electrolytic  dissociation  and  the  law  of  mass  action.  If 
the  electrolyte  is  completely  dissociated  into  two  ions, 
the  product  of  the  active  masses  must  be  constant,  and 
equal  to  the  square  of  the  solubility  of  the  salt  before  any 
second  compound  is  added.  If  m  is  the  solubility  of  the 
salt  after  a  second  salt  with  a  common  ion  is  added,  x  the 
amount  added,  and  mQ  the  solubility  of  the  salt  alone,  we 
have : — 

m  ( m  4-  x)  =  m}. 

But  since  the  solutions  are  only  partly  dissociated,  we 
must  take  into  account  the  amounts  of  dissociation.  Let 
«0  be  the  dissociation  of  the  original  substance  in  a  saturated 
solution,  ax  the  dissociation  of  this  substance  in  the  presence 
of  the  substance  added,  and  a  the  dissociation  of  the  added 
substance  ;  the  above  expression  then  becomes  :  — 

1  Ztschr.  phys.  Chem.,  4,  379. 


EVIDENCE  FOR  THE  THEORY  151 

ma  (ma 


The  effect  of  one  salt  on  the  solubility  of  another  with  a 
common  ion  was  tested  experimentally  by  A.  A.  Noyes.1 
He  worked  with  eleven  pairs  of  substances,  determined 
the  solubility  of  the  one  with  which  the  solution  was  satu- 
rated, added  the  second,  and  determined  the  change  pro- 
duced in  the  solubility.  He  then  calculated  the  solubility 
of  the  first  salt,  after  the  second  was  added,  from  the 
formula  of  Nernst,  and  compared  the  solubility  found  with 
that  deduced  theoretically.  There  is  a  general  agreement 
between  the  two  sets  of  values,  but  some  discrepancies 
appeared,  which  are  larger  than  could  be  accounted  for  by 
experimental  error. 

In  calculating  solubility  from  the  equation  of  Nernst,  we 
must  know  a,  alf  and  «0>  or  the  dissociations  of  all  the  solu- 
tions involved.  Noyes  concluded  from  his  work  that  the 
deduction  of  Nernst  is  perfectly  correct,  and  that  the  appa- 
rent differences  are  due  to  errors  in  the  determination  of 
the  dissociation  values.  The  relation  between  dissociation 
by  heat  and  electrolytic  dissociation,  as  effected  by  an 
excess  of  either  of  the  products  of  dissociation,  is,  there- 
fore, established. 

Determination  of  Electrolytic  Dissociation  by  Change  in 
Solubility.  —  The  slight  differences  between  the  solubilities 
found  experimentally  and  calculated,  led  Noyes  to  suspect 
that  the  conductivity  method  of  measuring  dissociation  was 
not  accurate.  He,  therefore,  reversed  the  above  procedure, 
and  used  solubility  measurements  to  determine  dissoci- 
ation. Knowing  the  dissociation  of  the  substance  in  the 

i  Ztschr.  phys.  Chem.,  6,  241. 


152  ELECTROLYTIC  DISSOCIATION 

saturated  solution,  and  the  change  in  the  solubility  of 
this,  substance  produced  by  adding  a  given  amount  of  the 
second  substance,  he  could  calculate  the  dissociation  of  the 
second  substance. 

A  condition  which  must  be  fulfilled  is,  that  the  salt  with 
which  the  solution  is  saturated  is  not  very  soluble,  since 
we  would  then  be  dealing  with  a  concentrated  solution,  to 
which  the  laws  here  involved  do  not  apply. 

Noyes  first  used  thallous  chloride  with  which  to  saturate 
his  solvent,  since  it  is  not  very  soluble ;  and  then  added 
to  this  a  number  of  soluble  chlorides,  as  potassium, 
sodium,  and  ammonium,  and  calculated  the  dissociation 
of  the  latter,  from  the  change  which  he  found  produced 
by  them  in  the  solubility  of  the  thallous  chloride.  He l  at 
first  obtained  dissociation  values  for  the  alkaline  chlorides 
and  other  compounds,  which  differed  considerably  from 
that  calculated  from  conductivity. 

Agreement  between  Dissociation  determined  by  Conduc- 
tivity, Freezing-point  Lowering,  and  Solubility.  —  We  had, 
then,  two  methods  of  measuring  electrolytic  dissociation, 
conductivity,  and  change  in  solubility,  and  the  two  gave 
values  which  did  not  agree.  The  question  arose,  which 
is  correct,  or  are  both  methods  to  be  discarded? 

At  this  time  H.  C.  Jones2  undertook,  at  the  suggestion 
of  Ostwald,  to  so  improve  the  freezing-point  method  of 
Beckmann,  that  it  could  be  applied  to  the  measurement 
of  electrolytic  dissociation.  A  thermometer  divided  into 
thousandths  of  a  degree  was  made,  and  carefully  standard- 
ized. The  apparatus  to  contain  the  liquid  was  enlarged 

1  Ztschr.  phys.  Chem.,  9,  603 ;  12,  162 ;  13,  412. 
8  Ibid.,  ii,  no,  529;  12,  623. 


EVIDENCE   FOR  THE  THEORY  153 

so  as  to  hold  a  litre.  The  air-bath  around  the  liquid 
was  enlarged,  and  a  number  of  precautions  taken  to' 
secure  more  accurate  determinations  of  the  temperatures 
at  which  both  solvent  and  solution  froze.  The  dissociation 
of  a  number  of  acids,  bases,  and  salts  was  worked  out  by 
this  improved  freezing-point  method,  over  a  considerable 
range  of  concentration.  The  result  was,  as  has  already 
been  seen  (p.  130),  a  satisfactory  agreement  between  the 
dissociation  calculated  from  freezing-point  lowering  and 
that  calculated  from  conductivity. 

In  calculating  dissociation  from  solubility,  Noyes  had 
assumed  that  the  thallous  chloride  was  dissociated  to  the 
same  extent  as  potassium  and  sodium  chlorides.  He 
afterwards  found1  that  this  assumption  was  not  correct. 
He  determined  the  dissociation  of  thallous  chloride, 
and  when  he  introduced  the  correct  values  for  this  com- 
pound into  the  calculation,  he  found  that  the  dissociation 
of  the  second  compound,  as  determined  by  solubility, 
agreed  very  satisfactorily  with  the  results  of  the  other  two 
methods. 

The  three  most  general  methods  of  measuring  electro- 
lytic dissociation  give,  then,  values  which  agree  very  well 
with  one  another.  This  fact  should  be  carefully  borne  in 
mind,  in  considering  the  evidence  bearing  upon  the  theory 
of  electrolytic  dissociation. 

The  Relation  between  the  Two  Kinds  of  Dissociation 
an  Analogy. — The  relation  which  has  just  been  pointed 
out,  between  the  dissociation  of  a  vapor  by  heat  and  elec- 
trolytic dissociation,  is  only  an  analogy.  The  processes 
are  not  at  all  identical,  as  is  shown  by  the  fact  that  the 

1  Ztschr.  phys.  Chem.,  16,  125. 


I  $4  ELECTROLYTIC  DISSOCIATION 

end  products  are  very  different.  Take  the  compound 
ammonium  chloride;  it  is  broken  down  by  heat  into 
ammonia  and  hydrochloric  acid :  — 


NH4C1  =  NH3  +  HC1. 

Both  of  these  are  in  the  molecular  condition,  and  can 
be  isolated. 

When  ammonium  chloride  is  dissociated  electrolytically 
by  water,  it  breaks  down  thus  :  — 

NH4C1  =  N+H4  +  Cl. 

The  composition  of  the  products  is  not  only  different 
from  the  first  case,  but  both  the  ammonium  and  chlorine 
exist  as  ions,  the  one  charged  positively  and  the  other 
negatively,  and  neither  can  be  isolated  as  such.  That 
there  is  some  deep-seated  connection  between  the  two 
processes  is  probable.  Fused  salts  often  conduct  the 
current  just  as  they  would  do  if  dissolved  in  water.  But 
we  must  leave  it  for  the  future  to  show  the  exact  nature  of 
the  connection  between  the  two  kinds  of  dissociation. 

DISSOCIATION   AND    CHEMICAL    ACTIVITY 

Perhaps  the  most  interesting  test  of  the  theory  of  elec- 
trolytic dissociation  yet  remains.  If  the  properties  of 
dilute  solutions  of  electrolytes  are,  in  general,  properties 
of  the  ions,  what  must  be  said  in  reference  to  the  property 
of  such  solutions  to  react  chemically.  If  there  are  only 
ions  present  in  the  solutions,  it  is  clear  that  any  chemical 
reaction  which  may  take  place  is  a  reaction  between  ions 
only.  If  the  solution  contains  molecules  as  well  as  ions, 


EVIDENCE   FOR  THE  THEORY  155 

the  chemical  reactivity  may  be  due  to  the  molecules,  or  it 
may  be  due  to  the  ions,  or  it  may  be  due  to  both.  The 
problem  is  not  only  of  interest  from  the  physical  chemical, 
but  is  of  the  very  highest  importance  from  the  purely 
chemical,  standpoint. 

The  number  of  possible  cases  by  which  the  relation 
between  dissociation  and  chemical  activity  can  be  investi- 
gated is  very  large.  We  will  take  several  acids,  inorganic 
and  organic,  and  a  few  bases  which  have  been  worked 
out  thoroughly  in  this  connection.  The  method  of  attack- 
ing the  problem  is  comparatively  simple.  The  dissocia- 
tion of  substances  must  be  determined,  also  their  power 
to  react  chemically.  Then  the  two  must  be  compared. 

Conductivity  and  Reaction  Velocity.  —  Here,  again,  we 
are  indebted  for  our  knowledge  chiefly  to  Ostwald.  In  a 
paper  on  the  catalysis  of  methyl  acetate,1  he  expressed  the 
opinion  that  the  velocity  with  which  acids  would  invert 
cane-sugar,  like  other  reactions  of  acids,  depends  only  on 
their  affinity.  In  a  later  paper,2  describing  work  along 
this  line,  this  view  was  substantiated.  It  then  remained 
to  determine  whether  there  was  any  relation  between  these 
two  reactions  produced  by  different  acids,  and  the  disso- 
ciation of  the  acids  themselves.  The  following  table,  taken 
from  Ostwald's  Lehrbuch,3  gives  a  direct  comparison  of  the 
conductivities  of  a  number  of  acids,  with  their  power  to 
saponify  methyl  acetate,  and  to  invert  cane-sugar. 

Column  I  gives  the  conductivities  of  the  acids  referred 
to  hydrochloric  acid  as  100;  column  II,  the  velocities  with 

which  they  effect  the  catalysis  of  methyl  acetate;    and 

» 

l  Journ.  prakt.  Chem.  [2],  28,  495.  2  Ibid.,  29,  385. 

3  Lehrb.  allg.  Chem.,  II,  p.  650. 


i56 


ELECTROLYTIC  DISSOCIATION 


column   III,  the  velocities  with  which  they  invert  cane- 
sugar. 

Hydrochloric  acid, 

Hydrobromic  acid, 

Nitric  acid, 

Sulphuric  acid, 

Formic  acid, 

Acetic  acid, 

Monochloracetic  acid, 

Dichloracetic  acid, 

Trichloracetic  acid, 

Oxalic  acid, 

Malonic  acid, 

Succinic  acid, 

Malic  acid, 

Tartaric  acid, 

Racemic  acid, 

Ostwald  adds,  that  when  we  consider  that  neither  the 
temperature,  nor  the  dilution,  is  the  same  in  the  three 
series,  the  agreement  is  satisfactory. 

Ostwald  studied  also  other  reactions  in  which  acids  are 
involved,  such  as  the  velocity  with  which  they  dissolve 
calcium  oxalate,  or  the  way  in  which  they  divide  a  base 
between  them.  He  found,  in  all  of  these  cases,  exactly  the 
same  order  of  avidity  as  given  above. 

A  little  later  he  carried  out  an  investigation  strictly 
analogous  to  the  above,  using  a  number  of  bases.  The 
reaction  studied  was  the  velocity  with  which  bases  sapon- 
ify ethyl  acetate.  The  relative  reaction  velocities  and 
conductivities  are  given  in  the  following  table.  Column  I 
gives  the  reaction  velocities;  column  II,  the  conductivities. 


I 

ii 

in 

IOO.OO 

IOO.OO 

IOO.OO 

IOI.OO 

98.00 

III  .00 

99.60 

92.00 

IOO.OO 

65.10 

73-9° 

73.20 

1.68 

1.31 

1.53 

0.42 

o.34 

0.40 

4.90 

4-30 

4.84 

25-30 

23.00 

27.10 

62.30 

68.20 

75-40 

19.70 

17.60 

18.60 

3.10 

2.87 

3.08 

0.58 

0.50 

0-55 

1-34 

1.18 

1.27 

2.28 

2.30 

— 

2.63 

2.30 

— 

EVIDENCE   FOR  THE  THEORY  157 

I  II 

Potassium  hydroxide,  161.00  161.00 

Sodium  hydroxide,  162.00  149.00 

Lithium  hydroxide,  165.00  142.00 

Ammonium  hydroxide,  3.00  4.08 

Methylamine,  19.00  20.02 

Ethylamine,  19.00  20.05 

Propylamine,  18.06  18.04 

Amylamine,  4.00  6.09 

Dimethylamine,  22.00  23'°5 

Diethylamine,  26.00  28.03 

Trimethylamine,  7.03  9.07 

Triethylamine,  22.00  20.02 

Tetraethyl  ammonium  hydroxide,    131.00  128.00 

The  agreement  is  as  satisfactory  as  the  conditions  of 
work  would  allow  us  to  expect. 

Dissociation  measured  by  Chemical  Activity.  —  We  have 
just  seen  that  there  is  proportionality  between  dissociation 
and  chemical  activity,  and  that,  therefore,  the  amount  of 
dissociation  may  be  used  as  a  measure  of  the  chemical 
activity  of  electrolytes. 

This  process  can,  on  the  other  hand,  be  reversed,  and 
the  chemical  activity  of  substances  be  used  as  a  measure 
of  their  electrolytic  dissociation.  The  conductivity  and 
freezing-point  are  the  most  convenient  and  general  methods 
for  measuring  electrolytic  dissociation,  but  there  are  cases 
to  which  neither  of  these  can  be  applied.  It  is  sometimes 
desired  to  know  the  amount  of  the  dissociation  of  some 
acid,  in  the  presence  of  other  electrolytes  like  the  salts. 
Since  all  of  the  electrolytes  present  would  take  part  in  the 
conductivity,  and  in  the  lowering  of  the  freezing-point  of 
the  solvent,  it  would  be  difficult,  if  not  impossible,  to  deter- 


158  ELECTROLYTIC   DISSOCIATION 

mine  the  amount  of  the  dissociation  of  the  acid  by  means 
of  either  of  these  methods. 

Some  method  must  be  employed  which  will  detect  one 
kind  of  ions  in  the  presence  of  others.  The  chemical 
reactivity  of  the  hydrogen  ion  has  been  made  use  of  to 
solve  the  above  problem.  The  rate  at  which  cane-sugar 
is  inverted  by  hydrogen  ions  can  be  determined  very 
easily,  and  this  reaction  has  been  used  by  Trevor,1  and 
others,  to  measure  the  number  of  hydrogen  ions  present. 

Similarly,  the  specific  chemical  reactions  of  other  ions 
have  been  used  to  determine  the  amount  of  these  which 
are  present,  when  more  direct  methods  are  not  applicable. 
Thus,  the  dissociation  of  bases  can  be  measured  by  the  rate 
at  which  the  hydroxyl  ions  saponify  an  ethereal  salt.  These 
examples  suffice  to  show  the  proportionality  between  dis- 
sociation and  chemical  activity,  and  that  either  may  be 
used  as  a  measure  of  the  other. 

Chemical  Reactions  usually  take  place  between  Ions.  — 
The  facts  just  pointed  out  show  that  chemical  reactions,  in 
which  acids  and  bases  are  involved,  are  reactions  effected 
by  ions.  The  number  of  reactions  in  which  ions  are 
known  to  take  part  is  very  great,  including  by  far  the 
majority  of  the  cases  with  which  we  have  to  deal. 

It  has  been  supposed  that  gases  do  not  conduct 
electricity,  and  are,  therefore,  undissociated.  Reactions 
between  gases  could  not  be  ionic,  if  this  were  true.  The 
recent  work  of  J.  J.  Thomson2  has  made  it  very  probable 
that  gases  are  dissociated,  to  some  extent,  and  reactions 
between  gases  may  be  reactions  between  ions  only.  Thom- 
son3 has  also  shown  that  atoms  of  elementary  hydrogen 

1  Ztschr.  phys.  Chem.,  10,  321.  2  Nature,  loc.  cit.  8  Ibid, 


EVIDENCE   FOR  THE  THEORY  159 

gas  behave  as  if  they  were  both  positive  and  negative,  so 
that  it  is  not  improbable  that  reactions  between  the  parts 
of  elementary  gases  are  ionic,  but  this  is  far  from  proved. 
It  is  not  safe  to  conclude,  at  present,  that  all  chemical 
reactions  take  place  between  ions.  There  are  cases  known 
of  substances  which  conduct  very  little,  or  do  not  conduct 
at  all,  and  yet  react  chemically.  We  have  well  character- 
ized chemical  compounds,  formed  by  the  union  of  two  parts 
of  the  same  general  electrical  character.  Thus,  phos- 
phorus and  chlorine,  sulphur  and  chlorine,  chlorine  and 
bromine,  chlorine  and  iodine,  iodine  and  bromine,  combine  ; 
and  we  are  accustomed  to  regard  all  of  these  ions  as 
carrying  a  negative  charge.  But  in  this  connection  the 
question  arises,  whether  anion  and  cation  are  not,  after 
all,  only  relative,  one  ion  being  charged  more  or  less 
positive,  or  negative,  than  another. 

Reactions  between  organic  compounds,  in  general,  take 
place  much  more  slowly  than  between  inorganic,  and  the 
former  are  much  less  dissociated.  This  is  probably  due  to 
a  slow  progressive  dissociation  of  the  organic  substances, 
as  the  ions  already  present  enter  into  chemical  combina- 
tion. This  raises  the  question,  whether  in  those  reactions 
between  apparently  undissociated  substances,  there  are 
not  a  few  ions  present  which  react,  and  as  these  take  part 
in  the  reaction,  more  and  more  ions  are  slowly  formed, 
which  then  in  turn  react. 

Whatever  may  be  the  final  decision  as  to  whether  mole- 
cules can  take  part  in  chemical  reaction,  we  are  now  justi- 
fied in  stating,  that  most  of  the  chemical  reactions  with 
which  we  have  to  do  are  not  reactions  between  molecules, 
but  between  ions. 


I6O  ELECTROLYTIC   DISSOCIATION 

Dissociating  Power  of  Different  Solvents.  —  Different 
solvents  have  very  different  powers  of  breaking  down 
electrolytes  into  ions.  Water  is  the  strongest  dissociant 
known.  Of  the  more  common  solvents,  formic  acid  stands 
next  to  water  in  its  ionizing  power.  Then  come  methyl 
alcohol  and  ethyl  alcohol,  respectively,  then  acetone,  and 
finally  the  ethereal  salts  and  hydrocarbon,  which  have  very 
slight  dissociating  power. 

J.  J.  Thomson l  has  worked  out  an  ingenious  theory, 
which  will  be  considered  later,  connecting  the  dissociating 
power  of  solvents  with  their  dielectric  constants.  Experi- 
ment has  shown,  that  there  is  undoubtedly  a  qualitative 
relation  between  the  two,  but  there  does  not  seem  to  be  a 
proportionality.  This  is  shown  by  recent  work  on  the 
dissociating  power  of  formic  acid,2  and  of  methyl  and 
ethyl  alcohols.8  While  the  dissociating  powers  are  in 
general  in  the  same  order  as  the  dielectric  constants,  they 
are  not  proportional  to  them. 

If  water  has  such  remarkable  dissociating  power,  and  as 
chemical  activity  is  due  chiefly  to  ions,  water  should  play 
a  very  prominent  role  in  bringing  about  chemical  reaction. 
We  will  now  examine  a  number  of  cases  which  will  show 
whether  this  is  true. 

EFFECT   OF   WATER   ON    CHEMICAL    ACTIVITY 

Unless  very  special  precautions  are  taken  to  exclude 
moisture,  every  chemical  reaction  takes  place  in  the  pres- 
ence of  water.  This  is  largely  due  to  the  presence  of 
water-vapor  in  the  air,  which  permeates  everything  with 

1  Phil.  Mag.,  36,  320.  2  Zanninowich-Tessarin,  Ztschr.  phys.  Chem.,  19,  251. 

8  Jones,  Ztschr.  phvs.  Chrm.     Jubelband. 


EVIDENCE  FOR  THE  THEORY  l6l 

which  it  comes  in  contact.  Further,  when  a  solvent  other 
than  water  is  used,  water  is  often  formed  as  one  of  the 
products  of  the  many  reactions.  If  there  was  a  trace  of 
water-vapor  present  to  start  the  reaction,  the  quantity 
would  increase  rapidly  as  the  reaction  progressed. 

To  study  the  effect  of  water  on  chemical  activity,  we 
must  exclude  all  traces  of  moisture  at  the  outset,  and 
choose  reactions  in  which  no  water  is  formed.  We  must 
see  how  the  reaction  progresses  in  the  absence  of  water, 
then  admit  water,  and  see  what  difference  is  produced. 
This  is  the  method  which  has  been  employed,  and  it  has 
led  to  some  highly  interesting  and  surprising  results. 
Some  of  these  will  now  be  taken  up. 

Action  of  Dry  Chlorine  on  Metals.  —  Wanklyn1  passed 
dry  chlorine  over  fused  metallic  sodium,  and  found  that  no 
action  resulted.  The  melted  sodium  was  shaken  in  contact 
with  the  chlorine,  so  as  to  expose  a  fresh  surface  of  the 
metal.  Still  there  was  no  chemical  action  between  the 
two.  This  explains  the  frequent  failure  of  the  lecture 
experiment,  where  sodium  chloride  is  formed  by  the  direct 
union  of  sodium  and  chlorine.  If  the  lecturer  is  careful  to 
dry  the  chlorine  gas  which  is  passed  over  the  molten 
metal,  he  usually  observes  the  sodium  lying  in  the  same 
condition  after  the  experiment  as  before.  But  if  moisture 
in  any  way  is  admitted,  the  reaction  takes  place  with 
violence. 

Comper2  studied  the  action  of  dry  chlorine  on  a  number 
of  metals.  He  found  that  metallic  zinc  was  not  acted  on 
by  the  chlorine  at  first,  but  the  thin  zinc-foil  was  attacked 
after  a  time.  Metallic  magnesium  was  not  acted  upon  at 

i  Chem.  News,  20,  271  (1869).  2  Journ.  Chern,  Soc.,  43,  153  (1883). 


l62  ELECTROLYTIC  DISSOCIATION 

all,  and  metallic  silver  very  slowly.  Bismuth  was  appar- 
ently unacted  upon,  but  tin  was  rapidly  attacked.  Anti- 
mony and  arsenic  were  rapidly  acted  upon,  while  mercury 
was  acted  upon  as  rapidly  as  by  moist  chlorine. 

In  these  experiments  the  chlorine  was  dried  over  calcium 
chloride  for  some  days.  This  was,  evidently,  not  sufficient 
to  remove  the  last  traces  of  moisture,  so  that  the  chlorine 
used  by  Comper  was  only  partly  freed  from  water-vapor. 
It  would  be  of  interest  to  repeat  these  experiments  with 
perfectly  dry  chlorine. 

Comparative  Inactivity  of  Dry  Oxygen.  —  H.  B.  Baker1 
carried  out  a  number  of  experiments  with  carefully  dried 
oxygen,  which  led  to  results  of  very  considerable  impor- 
tance. The  gas  was  dried  by  allowing  it  to  stand  for 
a  long  time  in  the  presence  of  phosphorus  pentoxide. 
Moist  carbon,  in  the  presence  of  oxygen,  burned  with  the 
scintillation  characteristic  of  this  reaction.  A  certain 
amount  of  the  dried  carbon  was  burned  in  dry  oxygen,  but 
much  less  than  of  the  moist,  and  there  was  no  scintillation 
in  the  dry  oxygen.  Baker  concluded  from  a  number  of 
experiments,  that  pure  charcoal,  heated  in  oxygen  dried 
over  phosphorus  pentoxide,  does  not  burn  with  a  flame ; 
partial  combustion,  however,  goes  on,  both  carbon  monox- 
ide and  carbon  dioxide  being  formed.  Sulphur,  boron, 
amorphous  and  ordinary  phosphorus,  do  not  burn  in  dry 
oxygen.  Selenium,  tellurium,  arsenic,  and  antimony  show 
no  difference  in  their  combustion,  whether  the  oxygen  be 
moist  or  dry. 

Dixon2  studied  the  action  of  dry  oxygen  on  carbon 
monoxide,  under  the  influence  of  the  spark.  He  mixed 

1  Phil.  Trans.  (1888),  571.  2  Ibid.  (1884),  617. 


EVIDENCE  FOR  THE  THEORY  163 

three  volumes  of  carbon  monoxide  and  one  volume  of  dry 
oxygen,  and  passed  a  spark  through  the  mixture.  There 
was  no  explosion.  More  oxygen  was  then  added,  and 
again  the  spark  passed  without  explosion. 

A  fresh  charge  of  carbon  monoxide  was  then  prepared 
from  oxalic  acid,  and  an  excess  of  dry  oxygen  mixed  with 
it.  The  spark  passed  through  this,  also,  without  any  explo- 
sion. A  drop  of  water  was  then  added  to  the  mixture,  the 
spark  passed  and  there  resulted  the  usual  explosion. 

Experiments  were  then  carried  out  to  determine  the 
velocity  of  the  reaction,  as  affected  by  the  amount  of  steam 
present.  By  the  addition  of  steam  it  was  found  that  the 
velocity  of  the  reaction  increased  very  rapidly.  The  con- 
clusions from  this  work  were :  The  drier  the  carbon  mon- 
oxide and  the  oxygen,  the  less  the  tendency  to  unite ;  a  trace 
of  aqueous  vapor  causes  the  mixture  to  become  inflam- 
mable, and  the  velocity  of  the  reaction  increased  with  the 
amount  of  water  present. 

Dry  Hydrochloric  Acid  does  not  decompose  Carbonates.  — 
After  Wanklyn  had  showed  that  dry  chlorine  would  not  act 
on  fused  sodium,  and  Baker,  that  dry  oxygen  is  com- 
paratively inactive,  it  was  of  interest  to  test  the  chemical 
behavior  of  other  substances  when  free  from  moisture. 
One  of  the  most  vigorous  of  chemical  reactions  is  the 
decomposition  of  carbonates  by  strong  acids.  Hughes1 
studied  the  behavior  of  dry  hydrochloric  acid  toward 
carbonates,  to  see  what  influence  moisture  would  have  in 
such  a  reaction. 

Hydrochloric  acid  gas  was  dried,  by  passing  it  over 
sulphuric  acid  and  then  over  phosphorus  pentoxide.  It 

i  Phil.  Mag.,  34,  117  (1892). 


1 64  ELECTROLYTIC  DISSOCIATION 

was  then  brought  in  contact  with  carefully  dried  calcium 
carbonate.  A  few  results  will  show  the  amount  of  car- 
bonate decomposed.  In  one  experiment:  — 

Amount  of  carbonate  used      .......  0.8705  g. 

Weight  of  carbonate  after  treating  with  dried 

hydrochloric  acid 0.8712  g. 

Increase  in  weight  .     .  ...     .     .*    .     .     .  0.0007  g. 

Percentage  increase V    .  0.08 

In  a  second  experiment  the  percentage  increase  in 
weight  was  o.i.  The  theoretical  increase  in  weight  for 
complete  transformation  is  29  per  cent. 

Moist  hydrochloric  acid  gas  was  then  passed  over  cal- 
cium carbonate  for  the  same  length  of  time,  when  more 
than  one  hundred  times  as  much  carbonate  was  decom- 
posed as  when  dry  hydrochloric  acid  gas  was  used.  The 
experiment  was  then  performed  just  as  above,  using 
witherite  (BaCO3)  instead  of  calcite.  The  result  of  one 
experiment  is  given  :  — 

Amount  of  witherite  used 0.9976  g. 

Weight  after  treating  with  dried  hydrochloric 

acid  gas    .    .    .     .     .     .     .    .     .     .     .     .'  0.9984  g. 

Increase  in  weight 0.0008  g. 

Percentage  increase 0.08 

The  theoretical  increase  in  weight,  if  all  of  the  carbonate 
is  transformed  into  chloride,  is  14.7  per  cent. 

Hughes  concluded  from  his  work,  that  the  increase  in 
the  weight  of  the  carbonate,  after  passing  a  stream  of  dry 
hydrochloric  acid  over  it,  was  so  small,  that  no  definite 
proof  was  furnished  of  any  action  having  taken  place. 


EVIDENCE   FOR  THE  THEORY  165 

The  slight  variations  observed  may  be  due  to  experimental 
errors,  or  to  the  imprisonment  or  entanglement  of  the 
molecules  of  hydrochloric  acid  gas  amongst  the  finely 
powdered  particles  of  Iceland  spar,  or  witherite. 

Dry  Acids  exert  no  Action  on  Litmus  and  do  npt  form 
Salts.  —  Blue  litmus  is  not  changed  to  red  in  a  stream  of 
dry  hydrochloric  acid  gas.  Gore  has  shown  that  dry 
liquefied  hydrochloric  acid  has  no  action  on  litmus.  Marsh 
has  proved  that  glacial  acetic  acid,  which  is  perfectly  free 
from  moisture,  has  no  action  on  litmus.  Marsh 1  has  also 
shown  that  pure  sulphuric  acid,  free  from  every  trace  of 
moisture,  does  not  act  on  blue  litmus,  and,  further,  is 
probably  incapable  of  forming  salts.  And  Veley2  has 
proved  that  nitric  acid,  free  from  moisture  and  from  nitrous 
acid,  is  probably  incapable  of  forming  salts. 

Dry  Hydrochloric  Acid  does  not  precipitate  Silver  Nitrate 
in  Ether  or  in  Benzene.  —  Silver  nitrate  was  dissolved  in 
anhydrous  ether,  and  in  benzene.  A  current  of  dried 
hydrochloric  acid  gas  was  passed  through  these  solutions 
for  an  hour.  There  was  no  precipitate  formed,  though  the 
solution  became  slightly  turbid.  When  the  silver  nitrate 
was  dissolved  in  absolute  alcohol,  a  more  decided  precip- 
itate was  formed  in  the  course  of  an  hour,  but  the  decom- 
position was  far  from  complete.  This  remarkable  result 
was  also  obtained  by  Hughes. 

Comparative  Inactivity  of  Dry  Hydrogen  Sulphide.  — 
Veley3  found  that  dry  hydrogen  sulphide  does  not  act  on 
quicklime,  and  this  led  Hughes  to  investigate  the  action 
of  dry  hydrogen  sulphide  upon  metallic  oxides. 

i  Chem.  News,  61,  2.  2  phil.  Trans.  (1891),  279. 

3  Journ.  Chem.  Soc.  (1885),  484;  Phii.  Mag.,  33,  471  (1892), 


1 66  ELECTROLYTIC  DISSOCIATION 

Magnesium  oxide  was  used.  Dry  hydrogen  sulphide 
was  passed  over  this,  and  the  increase  in  weight  ascertained. 
One  or  two  results  will  show  what  took  place :  — 

FIRST 

Weight  of  magnesium  oxide  used    .     -.  * ..    .     .     0.7597  g. 

Weight  after  passing  dry  hydrogen  sulphide     .     0.7600  g. 

Increase  in  weight  .     .     .....    ..     .     0.0003  g- 

SECOND 

Weight  of  magnesium  oxide  used    .....     0.6360  g. 

Weight  after  passing  dry  hydrogen  sulphide     .     0.6368  g. 

Increase  in  weight  ...;....     0.0008  g. 

In  both  cases  the  increase  in  weight  is  within  the  limit 
of  experimental  error.  The  change  from  the  oxide  to  the 
sulphide,  which  is  exothermic  and  would,  therefore,  be 
expected  to  take  place,  does  not  occur. 

A  drop  of  water  was  then  added  to  the  magnesium  oxide, 
and  dry  hydrogen  sulphide  passed  over  it  as  before. 
The  white  oxide  quickly  became  greenish  yellow,  and  the 
following  result  will  show  the  increase  in  weight  pro- 
duced. 

Weight  of  magnesium  oxide  and  water     .     .\  .     0.7235  g. 

Weight  after  passing  the  hydrogen  sulphide  gas     0.8435  g. 

Gain  in  weight f    .     o.  1 200  g. 

The  gain  in  weight,  which  expresses  the  amount  of  oxide 
transformed  into  sulphide,  is  from  200  to  400  times  as  great 
as  when  all  moisture  is  excluded. 

Similar  results  have  been  obtained  with  barium  oxide. 


EVIDENCE   FOR  THE  THEORY  1 67 

Dry  hydrogen  sulphide  has  no  action  upon  barium  oxide, 
from  15°  to  90°. 

Ferric  oxide  showed  a  slight  increase  in  weight  when 
dry  hydrogen  sulphide  was  passed  over  it.  But  this  was 
probably  due  to  the  incomplete  drying  of  the  oxide  of  iron. 

When  dry  hydrogen  sulphide  was  passed  over  paper 
which  had  been  moistened  with  lead  acetate  and  afterwards 
thoroughly  dried,  there  was  no  action  whatever.  Moist 
paper  containing  lead  acetate  was,  of  course,  acted  upon 
at  once.  By  passing  the  dried  gas  first  over  dry  paper, 
and  then  over  moist,  the  difference  in  the  action  is  very 
striking. 

The  same  experiment  was  performed,  -using  antimony 
trichloride  instead  of  lead  acetate.  The  dry  paper  was 
unaltered  by  the  dried  hydrogen  sulphide,  while  the  moist 
paper  was  immediately  turned  yellow.  The  same  experi- 
ment was  performed  with  salts  of  tin,  cadmium,  bismuth, 
silver,  copper,  mercury,  and  cobalt,  and  exactly  the  same 
results  were  obtained  in  all  cases. 

We  may  conclude,  in  general,  that  dry  hydrogen  sul- 
phide has  no  action  on  the  dry  soluble  salts  of  the  metals, 
but  if  moisture  is  present  a  change  takes  place  at  once. 

Hughes l  found  that  when  mercuric  chloride  is  dissolved 
in  absolute  alcohol,  a  current  of  dry  hydrogen  sulphide 
can  be  passed  for  fifteen  minutes,  without  producing  any 
change.  Afterwards  the  solution  became  slightly  turbid, 
then  pale  yellow,  dark  yellow,  and  finally  greenish  yellow. 
No  further  change  took  place  when  the  current  was  passed 
an  hour  and  a  half.  The  addition  of  a  small  amount  of 
water  changed  the  green  to  a  black  precipitate. 

i  Phil.  Mag.,  35,  531  (1893). 


1 68  ELECTROLYTIC   DISSOCIATION 

Other  Reactions  which  do  not  take  place  without  Water. 
—  According  to  Baker,1  sulphur  trioxide  does  not  combine 
with  dry  lime,  or  dry  copper  oxide. 

Dry  ammonium  chloride  may  be  sublimed  from  a  mix- 
ture of  this  salt  with  dried  lime,  without  ammonia  being 
liberated. 

Dry  hydrogen  and  chlorine  may  be  exposed  to  the 
sunlight  for  two  days,  without  anything  like  complete 
reaction  taking  place. 

Dry  ammonia  and  hydrochloric  acid  can  be  partially 
separated  from  a  mixture  of  these  gases,  when  oppositely 
charged  plates  are  placed  in  the  mixture,  the  ammonia  pass- 
ing to  the  negative  plate,  the  hydrochloric  acid  to  the  positive. 

Dry  Hydrochloric  Acid  does  not  act  on  Dry  Ammonia.  — 
The  heading  of  this  paragraph  must  be  a  surprise  to  any 
one  who  is  familiar  with  the  properties  of  these  gases,  and 
is  not  acquainted  with  the  experimental  work  which  has 
been  done  to  establish  this  fact. 

Hughes2  stated,  that  when  ammonia  is  dried  over  lime, 
and  hydrochloric  acid  is  dried  by  phosphorus  pentoxide, 
the  two  would  remain  in  the  presence  of  one  another  for 
24  hours,  without  any  deposit  being  formed,  even  upon  the 
sides  of  the  containing  tube. 

H.  B.  Baker3  published  a  very  careful  investigation  of 
this  point,  in  which  the  ammonia  and  hydrochloric  acid 
gases  were  dried  over  phosphorus  pentoxide,  and  brought 
together  in  such  a  manner  that  any  change  in  volume 
could  be  readily  observed.  He  concluded,  that  perfectly 
dry  ammonia  and  perfectly  dry  hydrochloric  acid  gas  are 
entirely  without  action  upon  one  another. 

1  Journ.  Chem.  Soc.,  65,  611.  2  £^.  cit.  3  journ.  Chem.  Soc.,  65,  611, 


EVIDENCE   FOR  THE  THEORY  169 

The  conclusion  of  Baker  was  called  in  question  by 
Gutmann.1  The  latter  claimed  that  ammonia  and  hydro- 
chloric acid  cannot  be  dried  over  phosphorus  pentoxide, 
since  the  gases  are  absorbed. 

Baker,2  in  reply,  shows  that  the  phosphorus  pentoxide 
used  by  Gutmann  must  have  contained  metaphosphoric 
acid.  And,  further,  that  Gutmann  did  not  take  sufficient 
care  in  drying  the  gases.  The  glass  apparatus  must  be 
carefully  heated  to  remove  the  moisture,  which,  as  is  well 
known,  clings  to  it  so  tenaciously,  and  is  -held  by  it  so 
persistently.  Baker  repeated  his  earlier  experiments, 
working  with  the  greatest  care,  and  found  that  his  original 
conclusion  was  confirmed  in  every  respect.  Dry  hydro- 
chloric acid  gas  does  not  combine  with  dry  ammonia  gas. 

If  this  fact  creates  surprise,  the  following  will  be  almost 
beyond  belief. 

Dry  Sulphuric  Acid  does  not  act  on  Dry  Metallic 
Sodium.  —  An  experiment  was  performed  before  the 
Chemical  Society  of  London,3  in  which  a  piece  of  metallic 
sodium  was  plunged  into  concentrated  sulphuric  acid. 
When  the  sodium,  wrapped  with  a  piece  of  wire  which 
served  as  a  handle,  was  immersed  in  the  acid,  there  was  a 
flash  of  light,  showing  incipient  reaction ;  then  there  was 
perfect  quiescence,  the  sodium  remaining  freely  suspended 
in  the  sulphuric  acid.  The  reaction  at  first  was  due  to  the 
presence  of  a  few  sodium  ions  on  the  surface  of  the  metal, 
produced  by  the  moisture  in  the  air,  to  which  it  was 
exposed  for  an  instant. 

No  one  should  repeat  this  experiment,  unless  the  greatest 

1  Liebig's  Ann.,  299,  3.  2  Journ.  Chem.  Soc.  (1898),  422. 

3  Proceed.  Chem.  Soc.  (1894),  p.  86. 


170  ELECTROLYTIC  DISSOCIATION 

precautions  are  taken  in  drying  both  the  sodium  and  the 
sulphuric  acid.  It  is  quite  evident  that  ordinary  methods 
of  drying  would  not  suffice. 

The  facts  which  have  been  cited  in  this  section  show 
conclusively  the  necessity  of  the  presence  of  water  in 
many  chemical  reactions.  The  question  still  remains,  why 
is  water  essential?  We  believe  we  have  the  answer,  in 
that  water  has  a  very  high  dissociating  power,  breaking 
down  the  molecules  into  ions,  which  then  react.  These 
facts  are  just  what  would  be  predicted,  if  the  theory  of 
electrolytic  dissociation  is  true. 

Conclusion.  —  Some  of  the  lines  of  evidence  bearing 
upon  the  theory  of  electrolytic  dissociation  have  been 
presented  in  this  chapter.  There  are  many  more  which 
might  be  adduced ;  but  it  seems  that  what  has  been 
presented  suffices  to  show  how  strong  the  evidence  is  in 
favor  of  the  truth  of  this  generalization.  It  has  already 
been  mentioned,  and  stress  should  be  laid  upon  it,  that 
there  are  facts  to  which  the  theory,  as  we  now  conceive  it, 
does  not  seem  to  apply.  But  the  evidence  in  favor  of 
the  theory  is  so  overwhelming,  in  comparison  with  the  few 
apparent  exceptions,  that  we  should  examine  the  latter 
very  closely  before  concluding  finally  that  they  are  real 
exceptions.  Without  for  a  moment  ignoring  the  facts  for 
which  the  theory  does  not  seem  to  entirely  account,  the 
writer  believes  that  the  evidence  in  favor  of  a  great 
generalization  being  expressed  by  the  theory  of  electro- 
lytic dissociation  is  as  strong  as  in  the  case  of  many  of 
our  so-called  laws  of  nature.  For  how  many  of  these 
apply  under  all  conditions,  and  are  entirely  free  from 
exceptions  ? 


CHAPTER    IV 

SOME  APPLICATIONS   OF  THE   THEORY  OF  ELECTROLYTIC 
DISSOCIATION 

IN  the  last  two  chapters  we  have  attempted  to  answer 
the  questions,  how  did  the  theory  of  electrolytic  dissocia- 
tion arise,  and  what  are  some  of  the  reasons  for  believing 
that  it  is  true  ?  There  still  remains  the  question,  of  what 
scientific  use  is  this  theory  ?  And  this  brings  us  to  the 
subject  of  our  last  chapter. 

Few  theories  have  ever  been  advanced  in  science  which, 
in  a  dozen  years,  have  found  wider  application  than  the 
theory  which  we  are  considering.  It  has  already  been 
applied  not  only  to  chemical  problems,  but  also  to  physical, 
and  to  biological  in  the  broadest  sense.  A  few  of  these 
applications  will  now  be  taken  up. 

APPLICATION   OF   THE   THEORY   OF   ELECTROLYTIC   DIS- 
SOCIATION  TO    CHEMICAL    PROBLEMS 

This  theory  has  never  directly  exercised  any  marked 
influence  on  the  study  of  the  relations  between  the  com- 
position and  constitution  of  pure  substances,  and  their 
properties.  This  is  obviously  true,  since  pure  substances 
are  undissociated. 

The  theory  has,  however,  had  an  indirect  influence  in 
this  direction.  It  has  opened  up  such  a  number  of 

171 


172  ELECTROLYTIC   DISSOCIATION 

entirely  new  fields  of  research,  that  it  has  detracted  from 
work  along  these  lines.  The  number  of  investigations  of 
relations,  such  as  the  above,  has  become  less  in  the  last 
few  years ;  and  although  an  elaborate  piece  of  work  has 
appeared  from  time  to  time,  the  physical  chemist  of  to-day 
finds  more  promising  lines  of  work  suggested  to  him  by 
the  newer  conceptions.  Without  detracting  for  a  moment 
from  the  value  of  the  enormous  amount  of  labor  spent  in 
studying  the  properties  of  pure  substances,  yet  it  should 
be  stated,  that  the  great  advances  in  the  last  few  years 
have  resulted  from  the  study  of  one  substance  in  the 
presence  of  another. 

THE    THEORY    OF    ELECTROLYTIC    DISSOCIATION    AS   APPLIED 
TO    SOLUTIONS 

It  will  be  remembered  that  van't  Hoff  showed  that 
solutions  behave,  in  certain  respects,  like  gases.  There  is 
an  analogy  between  the  gas  particles  distributed  in  space 
and  the  dissolved  particles  distributed  throughout  the 
solvent,  —  space  bearing  a  similar  relation  to  the  gas  that 
the  solvent  does  to  the  solution.  It  has  also  been  shown, 
as  stated  above,  that  it  is  in  solutions,  chiefly,  that  we  have 
molecules  broken  down  into  ions.  Further,  the  impor- 
tance of  a  thorough  study  of  solutions  becomes  at  once 
apparent,  when  we  consider  that  most  chemical  reactions 
take  place  in  solution.  This  is  especially  true  of  inorganic 
reactions,  most  of  them  taking  place  in  what  has  come 
to  be  known  as  the  wet  way.  And,  indeed,  in  organic 
chemistry,  also,  some  solvent  is  often  employed  which  has 
the  property  of  dissociating  to  some  extent  one  or  more  of 
the  substances  present. 


APPLICATIONS   OF  THE  THEORY  173 

We  know  matter  in  three  states  of  aggregation,  solid, 
liquid,  and  gas,  and  have,  therefore,  nine  classes  of 
solutions :  — 

Gas  in  gas  Gas  in  liquid  Gas  in  solid 

Liquid  in  gas  Liquid  in  liquid          Liquid  in  solid 

Solid  in  gas  Solid  in  liquid  Solid  in  solid 

Examples  of  all  of  these  nine  classes  are  known.  We 
can,  however,  from  the  standpoint  of  the  dissociation 
theory,  deal  best  with  solutions  in  liquids  as  solvents, 
and  we  will,  therefore,  limit  ourselves  to  solutions  of  this 
kind. 

Osmotic  Pressure.  —  Since  van't  Hoff1  pointed  out  the 
analogy  between  the  osmotic  pressure  of  dissolved  sub- 
stances and  the  gas  pressure  of  gases,  much  work  has 
been  done  on  methods  of  measuring  osmotic  pressure. 
Osmotic  pressure,  as  has  already  been  shown,  is  a  very 
difficult  quantity  to  measure  directly,  and  a  number  of 
comparative  methods  have  been  devised.  These  aim  to 
measure  the  relative  osmotic  pressures  exerted  by  different 
substances.  If  we,  then,  know  the  absolute  osmotic  press- 
ure of  any  one  of  these  substances,  we  can  calculate  the 
absolute  osmotic  pressure  of  all  the  others.  The  rel- 
ative method  of  De  Vries2  has  already  been  considered. 
Those  of  Tammann,3  Bonders  and  Hamburger,4  Wladimi- 
roff,5  and  Lob6  should  be  mentioned,  in  order  that  they 
may  be  examined,  if  desired.  These  methods  have  been 
applied,  not  only  to  non-electrolytes,  but  also  to  electro- 

1  Loc.  cit.  2  Loc.  cit.  3  Wied.  Ann.,  34,  299. 

4  Onders  Physiol.  Lab.,  Utrecht  (3),  9,  26;  Ztschr.  phys.  Chem.,  6,  319. 

5  Ztschr.  phys.  Chem.,  7,  529.  6  Ibid.,  14,  424. 


174  ELECTROLYTIC   DISSOCIATION 

lytes.  Since  an  ion  exerts  exactly  the  same  osmotic 
pressure  as  a  molecule,  when  we  determine  the  osmotic 
pressure  of  a  partly  dissociated  solution,  we  can  calculate 
the  amount  to  which  that  solution  is  dissociated.  We 
know,  from  the  study  of  non-electrolytes,  the  osmotic 
pressure  which  would  be  exerted  if  there  was  no  dissocia- 
tion ;  we  know  that  if  the  electrolytes  break  down  into 
two  ions,  that  the  solution  when  completely  dissociated 
would  give  twice  this  osmotic  pressure.  Knowing  the 
actual  osmotic  pressure  exerted,  we  can  calculate  the 
amount  of  dissociation  at  once.  Although  we  have  more 
accurate  methods  of  measuring  dissociation  than  the 
above,  yet  this  serves  to  confirm  the  results  of  other 
methods. 

Diffusion.  —  Our  knowledge  of  the  osmotic  pressure  of 
solutions  has  thrown  light  on  the  way  in  which  salts  diffuse 
in  solution.  It  is  well  known  that  a  salt  always  diffuses 
from  the  solution  into  the  pure  solvent,  or  from  a  more 
concentrated  to  a  more  dilute  solution ;  and  this  continues 
until  the  whole  has  become  homogeneous.  The  law  of 
diffusion  was  discovered  by  Fick.1  "The  amount  of  salt 
which  diffuses  through  a  given  cross-section  is  propor- 
tional to  the  difference  in  concentrations  of  two  cross- 
sections  lying  very  close  to  one  another."  Diffusion 
depends,  then,  upon  difference  in  concentration. 

The  fundamental  question  of  diffusion  is,  however,  still 
unanswered.  What  causes  it  ?  What  is  the  force  in 
operation  which  drives  the  dissolved  substance  from  one 
region  to  another  quite  remote,  if  the  solution  is  allowed 
to  come  in  contact  with  the  pure  solvent,  or  if  a  more 

1  Pogg.  Ann.,  94,  59  (1855). 


APPLICATIONS   OF  THE  THEORY  175 

concentrated  is  brought  in  contact  with  a  more  dilute 
solution  ? 

We  see  at  once  a  connection  between  the  law  of  diffu- 
sion and  that  of  osmotic  pressure.  Diffusion  depends 
upon  difference  in  concentration.  Osmotic  pressure  de- 
pends also  upon  difference  in  concentration,  and  a  quan- 
titative study  of  both  the  diffusion  and  osmotic  pressure  of 
non-electrolytes  and  electrolytes  has  shown  that  osmotic 
pressure  is  the  cause  of  diffusion.  Wherever  there  is  a 
difference  in  the  osmotic  pressure  of  two  solutions,  diffu- 
sion will  take  place  from  the  region  of  greater  into  that 
of  less  pressure,  if  the  two  solutions  are  brought  in  con- 
tact. This  is  analogous  to  the  diffusion  of  gases,  which 
always  takes  place  from  the  region  where  the  gas  exerts 
a  greater  pressure  to  the  one  where  the  pressure  is  smaller. 

But  there  exists  a  marked  difference  between  the  two 
kinds  of  diffusion.  With  gases  this  takes  place  very 
rapidly,  and  equilibrium  is  usually  established  in  a  short 
time.  But  diffusion  in  solution  proceeds  very  slowly,  and 
it  may  require  weeks  and  months  for  a  condition  of  equi- 
librium to  be  reached,  if  the  column  of  liquid  has  any 
considerable  length. 

Nernst1  has  worked  out  a  theory  of  diffusion  based 
upon  osmotic  pressure,  first  for  non-electrolytes,  which  are 
simpler  because  there  is  no  dissociation,  and  then  for  elec- 
trolytes, taking  into  account  their  dissociation.  This  leads 
to  the  conclusion,  that  the  forces  required  to  drive  dis- 
solved particles  through  the  solvent  at  any  appreciable 
velocity  are  enormous.  Ostwald2  has  calculated  that  the 
force  required  to  drive  60  grams  of  urea  through  water, 

1  Ztschr.  phys.  Chem.,  2,  613.  2  Lehrb.  allg.  Chem.,  I,  p.  697. 


176  ELECTROLYTIC   DISSOCIATION 

with  the  velocity  of  i  cm.  per  second,  has  the  value  of 
2500  million  kilograms.  He  suggests  that  the  cause  of 
this  is  the  very  fine  state  of  division  of  the  dissolved  sub- 
stance. The  force  required  to  throw  a  small  stone  with  a 
considerable  velocity  is  not  great.  But  powder  the  stone 
very  finely,  and  an  enormous  force  would  be  required  to 
project  the  particles  of  dust  with  the  same  velocity.  Now 
let  this  process  of  division  be  continued  until  the  mole- 
cules were  reached,  and  forces  of  the  above  order  of 
magnitude  would  be  required. 

The  principle  of  Soret,1  which  has  already  been  con- 
sidered, as  furnishing  evidence  for  the  applicability  of  the 
law  of  Gay  Lussac  to  the  osmotic  pressure  of  solutions, 
should  be  referred  to  again  in  this  connection.  The 
change  in  the  concentration  of  a  homogeneous  solution, 
produced  by  keeping  the  different  parts  at  different  tem- 
peratures, has  been  shown  to  agree  with  that  calculated 
from  the  above  law.  This  principle  applies  as  well  to 
solutions  which  are  dissociated  as  to  those  which  are  not, 
since  an  ion  exerts  the  same  osmotic  pressure  as  a  mole- 
cule, and  is,  therefore,  subject  to  the  same  law  of  diffusion. 

Lowering  of  Freezing-point.  — The  theory  of  electro- 
lytic dissociation  has  been  applied  to  the  lowering  of  the 
freezing-point  of  the  solvent  produced  by  the  dissolved 
substance.  Reference  has  already  been  made  to  this 
fact,  in  connection  with  the  evidence  bearing  upon  the 
theory.  It  was  there  shown  that  Arrhenius  proved  that 
the  values  of  the  coefficient  "/,"  calculated  from  freez- 
ing-point lowering,  agreed  with  those  calculated  from 
conductivity. 

1  Loc.  cit.,  see  p.  86. 


APPLICATIONS   OF  THE  THEORY  177 

The  freezing-point  method  was  used  for  a  long  time, 
chiefly  to  determine  the  molecular  weights  of  substances 
in  solvents  which  do  not  dissociate  them.  The  applicabil- 
ity of  the  freezing-point  method  to  the  problem  of  molec- 
ular weights  was  pointed  out  by  Raoult,1  several  years 
before  the  theory  of  electrolytic  dissociation  was  proposed. 
By  working  with  solvents  other  than  water,  such  as  formic 
and  acetic  acids,  benzene,  and  nitrobenzene,  he  was  able 
to  discover  certain  general  laws  of  the  freezing-point  low- 
ering of  solvents.  When  water  was  used  as  a  solvent, 
so-called  abnormal  values  were  obtained.  The  freezing- 
point  lowerings  were  usually  much  greater  than  would  be 
expected  from  what  was  found  in  other  solvents. 

The  experimental  method  used  at  first  by  Raoult  was 
necessarily  crude,  as  it  had  just  been  devised  by  him. 
This  has  since  been  very  greatly  improved  by  Beckmann.2 
And  the  method  of  Beckmann  has  been  enlarged  and 
improved  by  Jones,3  Loomis,4  Lewis,5  Ponsot,6  and  others. 
The  most  refined  of  all  is  probably  the  method  described 
very  recently  by  Raoult,7  in  which  he  has  utilized  the  best 
points  in  all  of  the  above-described  methods.  However 
this  may  be,  the  freezing-point  method  has  now  been 
developed  to  a  fair  degree  of  perfection. 

The  direct  object  in  improving  the  freezing-point  method 
was  not  the  determination  of  molecular  weights,  —  the 
method  of  Beckmann  would  suffice  for  this  purpose,  —  but 
to  measure  the  electrolytic  dissociation  of  acids,  bases,  and 


1  Ann.  Chim.  Phys.  [6] ,  2,  66 ;  Harper's  Science  Series,  IV,  71. 

2  Ztschr.  phys.  Chem.,  2,  638,  715 ;  7,  323.         5  Ztschr.  phys.  Chem.,  15,  365. 
8  Ibid.,  ii,  no,  529;  12,623;  18,  283.  6  Ann.  Chim.  Phys.  [7],  10,  79. 
*  Wied.  Ann.,  51,  500;  57,  495  ;  <5o,  523.            7  Ztschr.  phys.  Chem.,  27,  617. 

N 


1/8  ELECTROLYTIC   DISSOCIATION 

salts  in  water.    There  were  also  certain  theoretical  questions 
involved,  in  connection  with  the  freezing-point  constant. 

The  freezing-point  method  has  already  been  applied 
extensively  to  the  measurement  of  electrolytic  dissocia- 
tion, and  is  now  to  be  regarded  as  one  of  the  most  gen- 
eral methods  for  this  purpose.  The  results  obtained  by 
Jones,  compared  with  those  of  Kohlrausch  from  conduc- 
tivity, have  already  been  given. 

Ions  lower  the  freezing-point  of  a  solvent  exactly  the 
same  amount  as  molecules,  so  that  with  a  partly  disso- 
ciated electrolyte  we  have  the  sum  of  the  lowering  of  the 
molecules  plus  that  of  the  ions.  We  know,  however,  from 
non-electrolytes,  how  much  lowering  the  molecules  alone 
would  produce,  and  we  can  calculate  from  the  lowering 
found,  what  percentage  of  the  molecules  is  broken  down 
into  ions. 

The  application  of  the  freezing-point  method  to  the  prob- 
lem of  molecular  weights  in  solution  has  helped  to  solve 
a  large  number  of  questions,  especially  in  organic  chem- 
istry. But  from  a  physical  chemical  point  of  view,  the 
newer  application  of  the  freezing-point  method  to  the  de- 
termination of  electrolytic  dissociation  is  by  far  the  more 
important. 

Lowering  of  Vapor-tension,  Rise  in  Boiling-point.  - 
What  has  been  said  in  reference  to  the  lowering  of  the 
freezing-point  of  solvents,  can  be  applied  directly  to  the 
lowering  of  their  vapor-tension  by  substances  dissolved  in 
them.  Here,  again,  Raoult 1  did  much  of  the  pioneer  work. 
The  laws  of  the  lowering  of  vapor-tension,  or  rise  in  boiling- 

1  Ann.  Chim.  Phys.  [6],  15,  375;  Compt.  rend.,  104,  1430;  Harper's  Science 
Series,  IV,  97,  125. 


APPLICATIONS   OF  THE  THEORY  179 

point,  had  not  been  discovered,  mainly  because  dissociat- 
ing solvents  had  been  used.  Raoult  worked  with  solutions 
in  ether,  and  discovered  the  general  law  of  the  lowering 
of  vapor-tension  :  One  molecule  of  any  undissociated  sub- 
stance, dissolved  in  one  hundred  molecules  of  any  volatile 
liquid,  lowers  the  vapor-pressure  of  this  liquid  by  a  nearly 
constant  fraction  of  its  value. 

He  showed  how  the  lowering  of  vapor-tension,  like  the 
lowering  of  the  freezing-point,  can  be  used  to  determine 
the  molecular  weight  of  the  dissolved  substance. 

Beckmann l  improved  this  method  of  Raoult,  as  he  had 
improved  the  freezing-point  method.  Instead  of  measur- 
ing the  depression  of  the  vapor-tension,  he  determined  the 
rise  in  boiling-point,  —  a  quantity  which  could  be  much  more 
easily  and  accurately  ascertained.  The  Beckmann  method 
of  determining  molecular  weights  has  been  modified  by  a 
number  of  investigators.  The  more  important  of  these 
improvements  are  those  introduced  by  Hite,2  Jones,3  and 
Landsberger.4 

The  boiling-point  method,  like  the  freezing-point,  has 
been  applied  also  to  the  measurement  of  the  dissociation 
of  electrolytes.  The  freezing-point  method  can  be  used  in 
this  connection,  with  only  a  few  solvents,  since  many  of  the 
solvents  with  high  dissociating  power  freeze  at  a  tempera- 
ture which  is  too  low  to  deal  with  successfully  in  this  con- 
nection. Indeed,  the  freezing-point  method,  as  a  measure 
of  dissociation,  has  been  applied  mainly  to  aqueous  solu- 
tions. The  boiling-point  method  for  measuring  electrolytic 

1  Ztschr.  phys.  Chem.,  4,  532;  6,  437;  8,  223;  15,  656;  17,  107;  18,  473;  21,  239. 

2  Amer.  Chem.  Journ.,  17,  507. 

3  Results  will  appear  in  Ztschr.  phys.  Chem.     Jubelband. 

4  Ber.  d.  chem.  Gesell.,  31,  4^8. 


1 80  ELECTROLYTIC  DISSOCIATION 

dissociation  admits  of  much  wider  application.  It  can  be 
employed  with  formic  acid,  methyl  alcohol,  ethyl  alcohol, 
acetone,  etc.,  solvents  which  have  a  fairly  great  dissociating 
power. 

This  application  of  the  boiling-point  method  is  of  very 
considerable  importance,  since  it  is  the  only  method  avail- 
able for  measuring  accurately  the  dissociation  of  electro- 
lytes in  these  solvents.  The  conductivity  method  cannot 
give  very  close  results,  because  of  the .  difficulty  of  deter- 
mining the  value  of  the  molecular  conductivity  (/-too)  at 
complete  dissociation.  These  solvents  all  dissociate  so 
much  less  than  water,  that,  with  the  exception  of  formic 
acid,  the  dilution  at  which  the  dissociation  is  complete  is 
so  great  that  the  conductivity  method  does  not  give  accu- 
rate results.  The  impurities  in  the  solvents,  at  these  very 
high  dilutions,  also  render  the  results  imperfect. 

The  importance  of  measuring  dissociation  in  solvents 
other  than  water  will  be  evident,  when  we  consider  that 
this  is  the  first  step  toward  a  physical  chemistry  in  other 
than  aqueous  solutions.  And,  in  addition,  there  is  in- 
volved a  theoretical  question  of  interest  and  importance. 
J.  J.  Thomson  l  has  shown,  as  already  mentioned,  that  if 
the  molecules  are  held  together  by  the  attraction  of  oppo- 
sitely charged  parts,  and  if  the  molecules  are  broken  down 
into  these  parts  by  solvents,  the  dissociating  power  of  sol- 
vents should  stand  in  the  same  relation  as  their  dielectric 
constants. 

Jones2  has  measured  the  dissociation  of  a  number  of 
salts  in  methyl  and  ethyl  alcohol,  using  his  modification 

1  Phil.  Mag.,  36,  320. 

2  Results  will  be  published  in  Ztschr.  phys.  Chem.    Jubelband. 


APPLICATIONS  OF  THE  THEORY  181 

of  the  Beckmann  boiling-point  apparatus.  While  he  found 
a  qualitative  relation  between  the  dielectric  constants  of 
these  solvents  and  their  dissociating  power,  compared  with 
water,  a  proportionality  between  dielectric  constants  and 
dissociating  power  does  not  exist,  as  has  already  been 
stated. 

The  application  of  the  boiling-point  method  to  the  prob- 
lem of  electrolytic  dissociation  has  been  made  only  in  the 
last  year  or  two,  and  much  of  value  will  undoubtedly 
result  from  further  work  with  this  method.  It  would, 
doubtless,  have  been  applied  much  earlier,  but  for  the 
experimental  difficulties  involved.  The  method  at  first 
was,  of  course,  imperfect,  containing  a  large  number  of 
errors,  and,  further,  the  boiling-point  constants  of  solvents 
are  small,  and  therefore  the  quantity  to  be  measured  was 
always  small.  A  number  of  sources  of  error  have  now 
been  removed  from  the  boiling-point  method,  and  when 
all  the  details  are  carefully  observed,  and  the  entire  work 
carried  out  with  the  greatest  care  and  precaution,  results 
can  be  obtained  for  the  electrolytic  dissociation  in  the 
alcohols,  which  should  be  accurate  to  within  about  i  per 
cent. 

The  rise  in  the  boiling-point,  like  the  lowering  of  the 
freezing-point,  is  that  produced  by  both  molecules  and 
ions,  —  an  ion  lowering  the  boiling-point  to  the  same 
extent  as  a  molecule.  But  in  partly  dissociated  solutions 
we  know,  from  a  study  of  non-electrolytes,  the  rise  produced 
by  the  molecules.  We  know,  further,  that  if  the  mole- 
cules of  the  electrolyte  were  completely  broken  down  into 
two  ions  each,  the  rise  in  the  boiling-point  would  be  twice 
as  great  as  if  there  was  no  dissociation.  From  the  rise 


1 82  ELECTROLYTIC   DISSOCIATION 

actually  found,  we  can  calculate,  at  once,  the  percentage 
of  dissociation  of  the  solution  in  question. 

The  theory  of  electrolytic  dissociation  has  been  applied 
to  solutions,  in  a  much  wider  sense  than  would  be  inferred 
from  the  foregoing.  The  additive  nature  of  the  properties 
of  completely  dissociated  solutions  has  already  been  dis- 
cussed. It  is  not  necessary  to  deal,  moreover,  with  solutions 
of  only  one  electrolyte  in  a  solvent.  Two  or  more  electro- 
lytes can  be  brought  simultaneously  into  the  solvent,  and 
the  resulting  solution  studied.  The  effect  of  one  dis- 
sociated substance  on  another  with  a  common  ion  has 
already  been  indicated.  Some  interesting  properties  of 
solutions,  which,  when  mixed,  do  not  reciprocally  affect 
each  other's  properties,  have  been  worked  out  by  Arrhe- 
nius1  and  others.  Arrhenius2  worked  with  solutions  of 
acids,  and  termed  those  which  fulfil  this  condition,  "iso- 
hydric."  The  study  of  such  solutions  from  the  standpoint 
of  his  theory,  brought  out  much  of  interest. 

Then,  again,  we  are  not  limited  to  one  or  more  electro- 
lytes in  one  solvent.  We  can  have  one  or  several  electro- 
lytes, in  one  or  more  solvents ;  and  such  cases  have  been 
studied.  The  electrolytes  may,  or  may  not,  have  a  common 
ion,  or  the  solvents  may,  or  may  not,  be  mixable  with  each 
other.  The  number  of  possibilities  is  very  great,  and 
some  have  already  been  studied.  But  the  scope  of  this 
work  will  not  allow  further  detail. 

The  Theory  of  Electrolytic  Dissociation  as  applied  to 
Electrochemistry.  —  New  light  has  been  thrown  upon  this 
entire  field,  by  the  theory  of  electrolytic  dissociation. 
Many  facts  which  were  discovered  before  the  theory  was 

1  Wied.  Ann.,  30,  51.  2  Ztschr.  phys.  Chem.,  2,  284. 


APPLICATIONS   OF  THE   THEORY  183 

proposed,  have  now,  by  means  of  it,  been  correlated,  and 
rationally  explained. 

Electrolysis.  —  We  can  now  interpret  much  more  clearly 
the  phenomenon  of  electrolysis.  A  dilute  solution  of  an 
electrolyte  is  completely  dissociated ;  there  are  no  mole- 
cules present,  all  of  them  having  been  broken  down  into 
ions.  When  the  current  is  passed  through  such  a  solu- 
tion, it  directs  the  ions,  the  one  to  the  cathode,  the  other 
to  the  anode,  where  they  give  up  their  charges  and  sepa- 
rate in  the  atomic  or  molecular  condition.  There  appears 
to  be  a  marked  difference  between  the  way  in  which 
metallic  conductors  carry  the  current,  and  the  manner 
in  which  it  passes  through  a  solution  of  an  electrolyte. 
A  metal  wire  carrying  a  current  apparently  undergoes 
no  change  except  in  temperature,  while  a  solution  con- 
ducts only  by  undergoing  simultaneous  decomposition,  — 
the  positively  charged  parts  moving  in  one  direction,  the 
negatively  charged  in  the  other.  Although  there  is  appar- 
ently such  a  marked  difference  in  the  way  in  which  the 
two  classes  of  conductors  carry  the  current,  a  closer  study 
of  the  two  processes  brings  out  relations  between  them 
which  do  not  appear  on  the  surface.  Indeed,  the  work 
of  J.  J.  Thomson  has  made  it  probable  that  there  is  a 
close  relation  between  metallic  and  electrolytic  conduction. 
The  view  seems  to  be  gaining  ground  that  conduction  in 
metals  is  also  ionic,  the  ions  here  being,  of  course,  very 
much  more  restricted  in  their  movements. 

The  ions  into  which  electrolytes  dissociate  all  carry  the 
same  amount  of  electricity,  or  a  simple  rational  multiple  of 
this  unit  quantity.  This  was  discovered  early  in  the  cen- 
tury by  Faraday,  and  is  now  the  well-known  Faraday's 


1 84  ELECTROLYTIC   DISSOCIATION 

law.  All  univalent  ions  carry  the  same  amount  of  electric- 
ity. This  we  will  call  the  unit.  All  bivalent  ions  carry 
twice,  all  trivalent  ions  three  times  this  amount,  and 
so  on. 

This  was  proved  by  the  fact,  that  when  a  current  is 
passed  through  solutions  of  metallic  salts  containing  uni- 
valent, bivalent,  trivalent,  etc.,  metallic  ions,  the  quantities 
of  the  metals  which  separate  stand  in  the  same  relations 
as  their  chemical  equivalents.  Univalent  metals  separate 
in  the  ratios  of  their  atomic  weights,  bivalent  in  the 
ratios  of  one-half  their  atomic  weights,  trivalent  metals 
in  the  ratios  of  one-third  of  their  atomic  weights,  and 
so  on. 

This  connects,  directly,  the  charges  carried  by  the  ions 
with  their  valence.  The  combining  power  of  ions  is  condi- 
tioned by  the  amount  of  electricity  which  they  carry.  If 
they  carry  one  unit  of  electricity,  they  have  the  smallest 
valence  or  combining  power.  If  two  units,  they  have 
twice  the  combining  power ;  if  three  units,  three  times  the 
power  to  combine,  and  so  on. 

This  is  exactly  what  would  be  expected,  if  the  power 
to  enter  into  chemical  combination  was  the  attraction 
between  oppositely  charged  parts.  The  larger  the  charge 
carried  by  the  ion,  the  greater  its  combining  power.  We 
may  now  say  that  chemical  valence  is  conditioned  by  the 
amount  of  electricity  carried  by  the  ion,  and  we  thus  give 
a  more  definite  and  precise  meaning  to  a  term  which  has 
hitherto  been  characterized  chiefly  by  vagueness  and 
obscurity. 

The  law  of  Faraday,  which  applies  to  the  amount  of 
electrical  energy  carried  by  the  ions,  has  its  analogue  in 


APPLICATIONS   OF  THE  THEORY  185 

the  law  of  Dulong  and  Petit,  which  says,  that  the  capacity 
for  heat  energy  is  the  same  for  all  atoms. 

After  the  law  of  Faraday  had  been  shown  to  be  a  true 
expression  of  the  amount  of  electricity  carried  by  ions,  it 
became  a  matter  of  importance  to  determine  the  amount 
of  electricity  carried  by  some  unit  quantity  of  ions.  The 
most  convenient  quantity  to  use  was  the  atomic  weight  of 
the  element  in  grams.  The  problem,  then,  was  to  deter- 
mine the  amount  of  electricity  which  would  electrolyze 
a  gram-atomic  weight  of  a  univalent  metal,  or  half  a 
gram-atomic  weight  of  a  bivalent  metal.  This  quantity, 
termed  the  "  electrochemical  equivalent,"  has  been  worked 
out  with  great  care,  and  with  the  following  result :  To 
separate  a  gram-atomic  weight  of  a  univalent  element 
like  silver,  requires,  in  round  numbers,  96,540  coulombs  of 
electricity  —  more  accurately  96,537  coulombs.  This  value 
is  given  to  show  the  enormous  charges  carried  by  the  ions, 
and  also  for  future  reference. 

The  large  amount  of  electrical  energy  carried  by  the  ions 
explains  the  great  difference  between  the  properties  of 
atoms  or  molecules,  and  ions.  Potassium,  sodium,  and  such 
substances,  when  present  in  the  metallic  or  molecular  con- 
dition, act  upon  water  with  great  vigor,  while  potassium  and 
sodium  ions  are  perfectly  inactive  toward  water.  The  same 
distinction  applies  to  a  large  number  of  other  substances. 

The  failure  to  recognize  the  distinction  between  atoms 
or  molecules,  and  ions,  that  the  one  is  charged  and  the 
other  not,  led  to  confusion  in  the  early  days  of  the  theory 
of  electrolytic  dissociation.  This  distinction,  however,  has 
so  often  been  insisted  upon,  that  it  is  now  pretty  generally 
understood.  ' 


1 86  ELECTROLYTIC  DISSOCIATION 

When  electrolytes  are  decomposed  by  the  current,  the 
ions  may  give  up  their  charges  and  separate  on  the  elec- 
trodes as  metallic  ions  do,  yielding  the  free  metal.  Or  the 
ion  may  be  of  such  a  nature  that  when  it  loses  its  charge, 
and  passes  over  into  the  atom,  or  group  of  atoms,  this 
may  act  chemically  upon  the  water  present,  and  decom- 
pose it.  Thus,  when  a  sodium  salt  is  electrolyzed,  the 
sodium  ion  gives  up  its  charge  to  the  cathode  and  becomes 
an  atom.  But,  of  course,  free  sodium  cannot  exist  as  such 
in  the  presence  of  water.  It  decomposes  water,  forming 
sodium  hydroxide,  and  hydrogen  gas  separates  from  the 
cathode :  — 

Na  +  HOH  =  NaOH  +  H. 

This  is  true  of  a  large  number  of  ions.  When  they  lose 
their  charge,  they  act  upon  the  water  present.  When  an 
acid  is  electrolyzed  the  hydrogen  ion  passes  to  the  cathode, 
gives  up  its  positive  charge  to  this,  and  escapes  as  hydro- 
gen gas.  The  anion,  whose  nature  depends  upon  the  acid 
used,  passes  to  the  anode,  and  gives  up  its  negative  charge 
(in  reality  takes  up  a  positive  charge).  The  anion,  after  it 
becomes  electrically  neutral,  decomposes  the  water  pres- 
ent. If  the  acid  is  hydrochloric,  the  free  chlorine  around 
the  anode  decomposes  water,  forming  hydrochloric  acid, 
and  sets  oxygen  free :  — 

2  Cl  +  H20  =  2  HC1  +  O. 

When  an  acid  is  electrolyzed,  we  thus  have  hydrogen 
set  free  at  one  pole  and  oxygen  at  the  other. 

It  may  be  said,  in  general,  that  anions,  after  they  have 
lost  their  charge,  are  incapable  of  existing  in  the  presence 


APPLICATIONS   OF  THE  THEORY  187 

of  water,  but  decompose  it  chemically,  setting  oxygen 
free.  A  current  can,  then,  be  passed  through  a  solu- 
tion of  an  electrolyte  in  only  one  way.  The  ions  must 
carry  the  electricity,  and  must  separate  at  the  electrodes 
after  losing  their  charge.  The  cation  may  separate 
directly,  as  the  metals  do,  or  it  may  act  upon  water, 
liberating  hydrogen.  The  anion,  after  losing  its  charge, 
usually  decomposes  water,  liberating  oxygen  at  the 
anode. 

The  decomposing  action  of  the  current  has  often  been 
used  to  determine  what  part  of  a  compound  forms  the 
cation,  and  what  part  the  anion.  The  principle  is 
simple.  The  electrolyte  is  dissolved  in  water,  and  the 
current  passed.  The  cation  moves  to  the  cathode,  the 
anion  to  the  anode.  After  electrolysis,  determine  what 
constituents  have  collected  around  the  two  electrodes ; 
that  around  the  cathode  is  the  cation,  that  around  the 
anode  is  the  anion.  In  all  acids  hydrogen  is  the  cation, 
and  the  remainder  of  the  molecule,  whatever  its  nature, 
forms  the  anion.  In  the  case  of  some  of  the  organic 
acids  the  anion  is  very  complex.  The  metal  in  salts  forms 
the  cation,  the  remainder  the  anion.  Bases  dissociate  into 
a  hydroxyl  anion,  and  the  remainder  forms  the  cation. 
The  characteristic  ion  of  acids  is  hydrogen,  of  bases  is 
hydroxyl.  This  same  method  of  determining  how  a 
molecule  will  dissociate  has  been  applied  also  to  very 
complex  cases.  How  will  compounds  like  K4Fe(CN)6, 
K2PtCl6,  KMnO4,  dissociate;  what  will  be  the  cation, 
and  what  the  anion?  This  has  been  determined  by 
electrolyzing  solutions  of  these  salts.  We  would  expect 
that  all  of  the  metals  would  go  to  the  cathode,  and  the 


1  88  ELECTROLYTIC  DISSOCIATION 

remainder  of  the  compounds  to  the  anode.      These  com- 
pounds, however,  dissociate  as  follows:  — 


K4Fe(CN)6=K4  +  Fe(CN)6. 
K2Pt(Cl)6=K2  +  PtCl6. 
KMn04=K  +  Mn04. 

These  examples  serve  to  show  the  relative  nature  of 
cation  and  anion.  What  is  a  cation  under  one  condition, 
may  be  a  part  of  an  anion  under  other  conditions.  Take 
the  above  cases,  iron  in  iron  salts  is  always  the  cation, 
and  this  applies,  also,  to  platinum  and  manganese.  But 
in  these  complex  salts,  where  there  is  a  more  positive  ion 
present,  such  as  potassium,  these  three  metals  become, 
respectively,  a  part  of  the  anion.  A  number  of  other 
cases,  similar  to  these,  have  been  worked  out,  and  many 
interesting  results  have  been  found. 

A  fact  of  unusual  interest  in  connection  with  the 
charge  which  ions  may  carry  has  been  pointed  out  by 
Ostwald.1  An  ion  having  exactly  the  same  chemical  com- 
position may  carry  different  charges  under  different  con- 
ditions. The  ion  (FeCN6)  may  carry  four  charges,  as  it 
does  if  it  comes  from  the  compound  K4Fe(CN)6,  or  it  may 
have  only  three  charges,  if  it  is  a  product  of  the  dissociation 
of  K3Fe(CN)6.  Similarly,  the  ion  MnO4  is  univalent,  if  it 
comes  from  the  compound  KMnO4,  and  bivalent  if  from 
K2MnO4.  As  Ostwald  points  out,  these  are  especially 
interesting  cases  of  isomerism,  since  it  cannot  be  referred 
to  a  different  "position  of  the  atoms."  The  only  differ- 

i  Lehrb.  allg.  Chem.,  II,  p.  588. 


APPLICATIONS   OF  THE  THEORY  189 

ence  here  is  in  the  charges  which  the  ions  carry.  The 
properties  of  MnO4  are  very  different  from  MnO4. 
Trivalent  iron,  manganese,  cobalt,  etc.,  have  very  different 
properties  from  bivalent,  and  there  is  no  more  reason  to 
expect  them  to  have  the  same  properties,  than  to  expect 
that  red  phosphorus  would  have  the  same  properties  as 
yellow.  In  both  cases  there  is  a  different  amount  of 
energy  present.  This  is  proved  by  electrolysis  for  iron, 
manganese,  etc.,  compounds.  Only  two-thirds  as  much 
ferric  iron  will  separate  for  a  given  current  as  ferrous,  and 
the  same  applies  to  the  other  compounds.  That  there  are 
different  amounts  of  energy  in  the  two  modifications  of 
phosphorus,  is  shown  by  their  heats  of  combustion,  which 
are  very  different. 

The  ions  with  the  larger  charge  usually  tend  to  lose 
some  of  it,  and  pass  over  into  the  condition  where  they 
carry  less  electricity.  Many  of  the  phenomena  which  we 
describe  as  oxidation  and  reduction  are  due  only  to  the  in- 
crease and  decrease,  respectively,  of  the  electrical  charges 
upon  the  ions,  —  a  ferrous  ion  passes  over  into  a  ferric  by 
taking  up  one  positive  charge ;  a  cupric  ion  becomes  a 
cuprous  ion  by  losing  one  positive  charge. 

Modes  of  Ion  Formation.  —  We  have  spoken  of  molecules 
dissociating  directly  into  two,  three,  and  more  ions,  and 
have,  perhaps,  left  the  impression  that  electrolytic  dissocia- 
tion can  take  place  in  only  one  way.  There  are,  however, 
a  number  of  ways  in  which  molecules  can  break  down 
into  ions.  The  following  have  been  pointed  out  by  Ost- 
wald:1  — 

(i)  A  molecule  may  break  down  directly  into  an  equiva- 

1  Lehrb.  allg.  Chem.,  II,  p.  786. 


190  ELECTROLYTIC  DISSOCIATION 

lent  number  of  positive  and  negative  ions.  This  is  the 
case  when  acids,  bases,  and  salts  are  dissolved  in  water. 
The  amount  of  dissociation  depends  upon  the  dilution. 
Strong  acids,  strong  bases,  and  salts  are  completely  dis- 
sociated in  about  one  one-thousandth  normal  solutions; 
while  weak  acids  and  bases  are  completely  dissociated 
only  at  much  greater  dilutions. 

(2)  An    electrically    neutral    substance    may   take    the 
charge  from  an  ion  and  become  itself  an  ion,  while  the 
original  ion,  having  lost  its  charge,  becomes  electrically 
neutral.     The  example  given   by  Ostwald  is  that  of  one 
metal  displacing  another  from  its  salts.     When  a  bar  of 
zinc  is  immersed  in  a  solution  of  copper  sulphate,  the  zinc 
takes  the  positive  charge  from  the  copper,  becoming  zinc 
ions,   while  the   copper   ions,    having   lost  their   charge, 
separate  as  metallic  copper. 

(3)  One  neutral  substance  may  pass  over  into  positive 
ions,  while  another  neutral  substance  may  pass  over  into 
an  equivalent  of  negative  ions.     Metallic  gold  is  electri- 
cally neutral.     Chlorine,  when  dissolved  in  water,  does  not 
pass  over  into  the  ionic  condition.     But  when  metallic  gold 
is  brought  into  the  presence  of  chlorine  water,  the  gold 
passes  over  into  cations,  and  the  chlorine  into  an  equivalent 
of  anions. 

It  should  have  been  stated  earlier,  that  when  gold  dis- 
solves in  chlorine  water  auric  chloride  is  formed,  and, 
indeed,  this  compound  is  obtained  if  the  solution  is 
evaporated.  If  the  solution  is  dilute,  we  have  only  gold 
ions  and  chlorine  ions  present,  and  no  molecules  what- 
ever of  gold  chloride. 

Neither  the  gold  nor  the  chlorine  can  pass  into  ions 


APPLICATIONS   OF  THE  THEORY  191 

when  alone,  but  in  the  presence  of  each  other  they  both 
become  ions. 

(4)  An  ion  may  take  up  a  larger  charge  than  it  already 
carries,  converting  a  neutral  substance  into  an  ion  with  the 
opposite  charge.  Thus,  a  ferrous  ion  in  the  presence  of 
chlorine  becomes  a  ferric  ion,  the  chlorine  passing  from 
the  molecular  into  the  ionic  condition.  This  is  an  example 
of  a  large  number  of  reactions,  which  are  usually  termed 
processes  of  oxidation. 

But,  on  the  other  hand,  an  ion  may  lose  a  part  of  the 
charge  which  it  already  carries,  converting  a  neutral  sub- 
stance into  an  ion  of  the  same  electrical  character.  Thus, 
when  a  solution  of  potassium  manganate  is  treated  with 

chlorine,  the  MnO4  ions,  carrying  two  charges,  pass  over 

into  the  MnO4  ions  carrying  one  charge,  the  negative 
charge  which  it  has  lost  going  to  the  chlorine,  converting 
this  into  an  ion.  The  processes  where  ions  lose  part  of  the 
charge  which  they  already  carry  are  processes  of  reduction. 

These  methods  of  ion  formation  have  all  been  described 
by  Ostwald,1  as  already  stated,  and  the  above  examples 
are  those  which  he  has  chosen  to  illustrate  the  several 
processes. 

Velocity  of  Ions.  —  Whenever  a  current  is  passed 
through  a  solution  of  an  electrolyte,  there  is  a  mechanical 
movement  of  the  ions  toward  the  electrodes.  To  under- 
stand the  electrochemical  behavior  of  ions,  we  must  study 
the  velocities  with  which  they  move  through  solutions. 

If  we  pass  a  current  through  a  solution  of  copper 
sulphate,  using  copper  electrodes,  copper  will  be  deposited 

i  Loc.  cit. 


1 92  ELECTROLYTIC   DISSOCIATION 

on  the  cathode,  and  exactly  an  equal  amount  will  pass  into 
solution  from  the  anode.  The  total  amount  of  copper  in 
solution  will  thus  remain  constant,  but  the  color  of  the 
solution  in  the  neighborhood  of  the  anode  will  become 
deeper,  while  in  the  neighborhood  of  the  cathode  it  gradu- 
ally becomes  less  intense.  The  solution  becomes  more 
concentrated  in  copper  around  the  anode,  and  less  concen- 
trated around  the  cathode. 

If  platinum  electrodes  were  used  in  this  experiment, 
copper  would  separate  at  the  cathode,  and  since  there  is  no 
metallic  copper  present  to  pass  into  solution,  the  amount 
in  solution  would  become  constantly  less.  In  this  case  the 
color  would  disappear  more  rapidly  around  the  cathode. 

Relative  Velocity  of  Ions.  —  Hittorf 1  was  the  first  to  cor- 
rectly explain  this  phenomenon.  He  suggested  that  it 
was  due  to  the  different  velocities  with  which  the  anions 
and  cations  move.  How  this  explanation  can  account  for 
the  facts,  we  can  see  from  the  following  diagram,  which  we 
owe  in  principle  to  Ostwald.2 

In  the  following  figure,  /  represents  the  condition  in 
the  solution  of  the  electrolyte  before  the  current  has 
been  passed  through  it.  The  black  circles  represent  the 
anions,  and  the  white  circles  the  cations.  For  each  anion 
present  in  the  solution  there  is  a  corresponding  cation,  and 
neither  anions  nor  cations  have  separated  at  the  electrodes. 

Let  us  take  a  case  where  the  velocity  of  the  anion  dif- 
fers greatly  from  that  of  the  cation,  and  for  simplicity,  let 
us  say  that  the  velocity  of  the  anion  is  twice  as  great  as 

1  Pogg.  Ann.,  89,  177 ;  98,  i ;  103,  i ;  106,  337,  513.    Ueber  die  Wanderungea 
der  lonen,  Ostwald  Klassiker,  21  and  22. 

2  Lehrb.  allg.  Chem.,  II,  p.  595. 


•  o 

V 

•  o 

•  0 

•  o 

•  0 

•  o 

•  0 

•  o 

•  0 

•  o 
•  o 

•  Oj 

o' 

•  o 

o 

1                        1       /-I  

o 


194  ELECTROLYTIC   DISSOCIATION 

that  of  the  cation.  Pass  a  current  through  the  solution 
until  three  molecules  have  been  decomposed,  and  the  con- 
dition represented  in  II  will  exist.  Three  anions  will  have 
separated  at  the  anode,  and  three  cations  at  the  cathode. 
But  the  solution  will  have  become,  relatively,  more  con- 
centrated on  the  anode  side  of  the  middle  layer  marked  m. 

Of  the  three  molecules  which  have  separated  from  the 
solution,  two  have  come  from  the  cathode  (C)  side  of  the 
middle  layer  m,  and  one  from  the  anode  side  (A).  If  we 
divide  the  loss  around  the  cathode  by  the  total  number  of 
molecules  electrolyzed,  we  will  obtain  the  value  f.  If,  on 
the  other  hand,  we  divide  the  loss  around  the  anode  by 
the  total  number  of  molecules  electrolyzed,  the  result  is  J. 
But  these  two  values  stand  to  one  another  in  exactly  the 
same  relation  as  the  relative  velocities  of  our  anion  and 
cation.  From  this  we  can  make  two  general  statements. 
First,  to  find  the  relative  velocity  of  the  cation,  divide  the 
loss  around  the  anode  by  the  total  amount  of  electrolyte 
decomposed.  Second,  to  find  the  relative  velocity  of  the 
anion,  divide  the  loss  around  the  cathode  by  the  total 
amount  of  electrolyte  decomposed. 

There  are  thus  three  quantities  which  can  be  deter- 
mined experimentally :  the  change  in  concentration  around 
the  cathode,  the  change  in  concentration  around  the  anode, 
and  the  total  amount  of  the  electrolyte  decomposed.  It  is 
necessary  to  determine  only  two  of  these,  the  third  being 
obtained  by  difference. 

The  total  amount  decomposed  is,  from  Faraday's  law, 
proportional  to  the  amount  of  current  passed  through  the 
solution ;  and  this  is  ascertained  by  measuring  the  latter 
by  means  of  a  voltameter. 


APPLICATIONS   OF  THE  THEORY  195 

A  number  of  methods,  based  upon  the  above  principles, 
have  been  devised  for  measuring  the  relative  velocity  of 
ions.  The  solution  must  be  electrolyzed  in  part,  and  the 
apparatus  so  constructed  that  the  change  in  concentration 
can  be  measured.  To  accomplish  this,  the  parts  of  the 
solution  around  the  two  electrodes  must  not  be  allowed 
to  mix  after  the  current  is  passed,  or  even  while  the  cur- 
rent is  passing. 

A  number  of  forms  of  apparatus  were  devised,  and  used, 
by  Hittorf,  in  which  a  membrane  was  interposed  to  pre- 
vent the  parts  of  the  solution  from  mixing  again,  but  it 
has  been  found  that  the  membrane  affects  the  results 
obtained. 

Kistiakowsky l  has  devised  and  used  a  form  of  apparatus 
without  any  membrane,  and  thus  removed  this  source  of 
error.  Loeb  and  Nernst2  have  used  a  form  of  apparatus 
which  is  essentially  a  Gay  Lussac  burette.  The  electrode 
around  which  the  solution  becomes  more  concentrated  is 
placed  below,  and  the  electrolysis  is  interrupted  while  there 
is  still  an  unaltered  layer  of  solution  between  the  two 
electrodes.  This  method  is  not  capable  of  any  very  high 
degree  of  accuracy,  since  there  is  no  means  by  which  the 
solutions  of  different  concentrations  can  be  completely 
separated  from  one  another,  removed,  and  analyzed.  The 
method  of  blowing  out  the  solution  around  the  anode, 
together  with  enough  of  the  unaltered  middle  layer  to 
wash  out  the  heavier  solution,  is  not  in  keeping  with  the 
most  refined  work.  From  work  on  this  problem,  which 
has  been  carried  out  in  this  University,  it  seems  to  be  far 
better  to  measure  the  amount  of  current  directly,  by  means 

1  Ztschr.  phys.  Chem.,  6,  97.  2  Ibid.,  2,  952. 


196  ELECTROLYTIC  DISSOCIATION 

of  a  voltameter,  than  by  an  indirect  method,  such  as  that 
used  by  Loeb  and  Nernst.  The  work  of  Bein,1  on  the 
relative  velocity  of  ions,  has  extended  over  a  number  of 
years,  and  very  recently  an  elaborate  investigation2  has 
been  published  by  him  on  this  problem.  The  forms  of 
apparatus  used  by  him  are  modifications  of  burettes,  some 
of  them  very  elaborate  and  complex.  The  work  of  Bein, 
taken  as  a  whole,  is  probably  the  best  which  has  ever  been 
done  on  the  relative  velocity  of  ions.  The  objection,  how- 
ever, to  the  apparatus  of  Loeb  and  Nernst,  seems  to 
apply  here  with  some  force.  There  does  not  seem  to  be 
any  means  of  completely  separating  the  solutions,  after 
the  electrolysis  is  brought  to  an  end. 

At  the  suggestion  of  the  writer,  W.  T.  Mather,3  working 
in  this  University,  undertook  to  devise  a  form  of  apparatus 
for  determining  the  relative  velocity  of  ions  which  would 
be  free  from  the  above-mentioned  objection. 

The  form  of  apparatus  which  he  constructed,  and  ap- 
plied successfully  in  a  few  cases,  consists,  essentially,  of 
two  upright  tubes  connected  by  a  U  tube,  which  joins  the 
upright  tubes  near  the  top.  In  the  centre  of  the  U  tube  a 
stop-cock  of  large  bore  is  introduced.  When  the  electrol- 
ysis has  proceeded  as  far  as  desired,  the  stop-cock  is 
closed,  and  then  the  solutions  in  the  two  arms  removed 
and  analyzed.  The  two  parts  of  the  solution  are  thus 
completely  separated,  which  is  not  possible  in  any  form 
hitherto  described. 

The  methods  just  described  have  to  do  only  with  the 

1  Wied.  Ann.,  46,  38. 

2  Ztschr.  phys.  Chem.,  27,  32 ;  28,  439. 

8  Dissertation,  Johns  Hopkins  University. 


APPLICATIONS   OF  THE  THEORY  197 

relative  velocities  with  which  the  ions  move,  and  con- 
siderable stress  has  been  laid  upon  this  point,  because 
of  a  generalization  which  has  been  reached  in  connection 
with  these  velocities. 

Kohlrausch^  s  Law  of  the  Independent  Migration  Velocity 
of  Ions.  —  F.  Kohlrausch 1  carried  out  a  beautiful  investi- 
gation on  the  power  of  solutions  of  electrolytes  to  conduct 
the  current,  which  will  be  referred  to  again.  The  con- 
ductivity of  a  solution,  referred  to  molecular  quantities,  he 
termed  its  "molecular  conductivity."  He  studied  the  con- 
ductivity of  solutions  at  different  dilutions,  and  found  that 
the  molecular  conductivity  increased  with  the  dilution,  up 
to  a  certain  point,  and  then  remained  constant,  no  matter 
how  far  the  dilution  was  carried  beyond  this  point.  This 
maximum  constant  value  of  the  molecular  conductivity  we 
will  call  /A^. 

Kohlrausch  observed  that  the  difference  between  the 
values  of  /*«,  for  two  electrolytes  with  a  common  anion 
and  different  cations  (say,  KC1  and  NaCl),  is  the  same  as 
the  difference  when  there  is  another  common  anion  and 
the  same  cations  as  before,  thus,  KNO3  and  NaNO3.  This 
will  be  seen  from  the  following  examples :  — 


DIFFERENCE 

KC1  ^  =  i, 

NaCl  M«=IJ 


|KN03          ft.  =  135-7  v 
i  Wied.  Ann.,  26,  160. 


22 


198  ELECTROLYTIC   DISSOCIATION 

Kohlrausch  concluded,  from  a  large  number  of  such 
facts,  that  the  value  of  /*«,  for  any  electrolyte  is  the  sum 
of  two  constants,  the  one  depending  upon  the  anion,  the 
other  upon  the  cation.  And  these  constants  are  the  same 
for  any  given  ion,  regardless  of  the  nature  of  the  other  ion 
which  is  present  in  the  solution. 

These  constants  are,  moreover,  the  velocities  of  the 
anions  and  cations  respectively,  and  thus  Kohlrausch  was 
led  to  his  law  of  the  independent  migration  velocities  of  ions. 

If  we  represent  the  velocity  of  the  cation  by  c,  and  of 

the  anion  by  a  :  — 

/*„  =  c  +  a. 

From  the  method  of  determining  the  relative  velocities, 
just  discussed,  we  determine  the  value  of  -.  Knowing 

c  4-  a  and  - ,  we  can  calculate,  at  once,  the  values  of  c 
and  a. 

The  absolute  velocity  of  ions  can  be  calculated  from  the 
law  of  Kohlrausch,  for  a  definite  fall  in  potential.  The 
absolute  velocity  of  at  least  one  ion  can  be  determined 
directly  by  experiment;  and  should  the  calculated  value 
agree  with  the  value  found,  it  would  argue  very  strongly 
in  favor  of  the  law  with  which  we  are  dealing. 

According  to  Kohlrausch,  the  absolute  velocities  of 
cation  and  anion  (c  and  a  respectively)  are  obtained  from 
the  relative  velocities  (c  and  a),  by  multiplying  by  a  factor. 
For  a  fall  in  potential  of  one  volt  per  centimetre  along  the 
tube,  or  a  potential  gradient  of  one  volt  per  centimetre, 
the  value  of  the  factor  is  iio.icr7.  The  absolute  velocity 
of  hydrogen,  as  calculated  by  Kohlrausch  for  the  above 
potential  gradient,  is  0.0032  cm.  per  second. 


APPLICATIONS  OF  THE  THEORY  199 

The  absolute  velocity  of  the  hydrogen  ion  has  been 
measured  directly  by  the  beautiful  experiment  of  Lodge.1 

A  glass  tube  8  cm.  wide  and  40  cm.  long  was  carefully 
graduated.  The  ends  were  bent  down  at  right  angles. 
The  tube,  placed  horizontally,  was  filled  with  gelatine  in 
which  sodium  chloride  was  dissolved.  This  material  was 
colored  red  by  a  little  phenolphthalem,  to  which  just 
enough  sodium  hydroxide  had  been  added  to  bring  out  the 
color.  The  ends  of  the  glass  tube  were  dipped  into  vessels 
filled  with  dilute  sulphuric  acid.  The  apparatus  was  then 
allowed  to  stand,  and  the  rate  ascertained  at  which  the 
acid  diffused  into  the  jelly.  The  current  was  then  passed 
from  one  vessel  containing  the  acid,  through  the  horizontal 
tube,  to  the  other  vessel.  The  hydrogen  ions  of  the  sul- 
phuric acid  move  with  the  current,  displace  the  sodium 
ions  from  the  salt,  and  form  hydrochloric  acid.  This 
decolorizes  the  phenolphthalem  in  the  jelly,  and  the  move- 
ment of  the  hydrogen  ions  can  thus  be  traced.  When  the 
proper  correction  is  introduced  for  diffusion,  we  have  at 
once  the  velocity  of  the  hydrogen  ion  for  the  potential 
gradient  used. 

Lodge  found,  in  three  experiments,  that  under  a  fall  of 
potential  of  one  volt  per  centimetre,  the  hydrogen  ion  has 
a  velocity  of  0.0029,  0.0026,  and  0.0024  cm.  per  second. 
This  value  agrees  very  closely  with  that  calculated  by 
Kohlrausch,  from  his  law  of  the  independent  migration 
velocity  of  ions. 

Whetham2  has  measured  the  absolute  velocity  of  a  few 
ions,  using  a  somewhat  different  method,  which  is,  how- 
ever, the  same  in  principle  as  that  of  Lodge.  The  ve- 

1  B.  A.  Report  (1886),  393.  2  Phil.  Trans.  (1893),  A.  p.  337. 


200  ELECTROLYTIC  DISSOCIATION 

locities  of  the  copper  ion,  and  the  Cr2O7  ion,  found  by 
Whetham,  agree  closely  with  those  calculated  from  the  law 
of  Kohlrausch. 

It  would  be  difficult  to  interpret  the  law  of  Kohlrausch, 
if  molecules  existed  as  such  in  very  dilute  solutions.  The 
law  is,  however,  not  only  explained  by  the  theory  of  elec- 
trolytic dissociation,  but  is  a  necessary  consequence  of  it. 
In  dilute  solutions,  the  molecules  are  completely  broken 
down  into  ions,  and  each  of  these  moves  through  the 
solution  with  a  velocity  which  is  definite  for  a  given  fall 
in  potential. 

The  law  of  Kohlrausch  applies  to  very  dilute  solutions 
of  strongly  dissociated  compounds.  It  holds,  at  medium 
dilution,  for  comparatively  few  substances,  and  does  not 
hold  at  all  for  the  weak  acids  and  bases.  How  are  these 
facts  to  be  explained  ? 

The  theory  of  electrolytic  dissociation  furnishes  not  only 
an  explanation  of  the  law,  but  an  equally  satisfactory 
explanation  of  the  exceptions. 

Those  solutions  to  which  the  law  applies  are  completely 
dissociated.  All  of  the  molecules  are  completely  broken 
down  into  ions,  and  all  of  the  ions  take  part  in  conducting 
the  current.  The  conductivity  is,  then,  a  maximum,  and 
gives  the  true  value  of  p^-  In  those  cases,  however,  where 
the  law  of  Kohlrausch  does  not  apply,  the  solutions  are 
not  completely  dissociated.  Some  of  the  molecules  are  not 
broken  down  into  ions,  and  these,  therefore,  take  no  part 
in  conducting  the  current.  The  molecular  conductivity  of 
such  solutions  is  not  the  maximum  conductivity  —  is  not 
the  true  value  of  /x^,  but  is  always  less.  This  applies  to 
the  fairly  concentrated  solutions  of  the  most  strongly  dis- 


APPLICATIONS  OF  THE  THEORY  2OI 

sociated  electrolytes,  and  even  to  the  very  dilute  solutions 
of  the  weakly  dissociated  electrolytes,  such  as  the  organic 
acids  and  bases. 

In  all  such  cases,  where  the  solutions  are  not  com- 
pletely dissociated,  we  must  take  into  account  the  amount 
of  the  dissociation.  When  •  this  is  done,  the  law  of 
Kohlrausch  becomes  much  more  general,  and  can  be 
applied,  as  Ostwald1  has  shown,  to  partially  dissociated 
solutions. 

If  we  represent  the  degree  of  dissociation  by  a,  the  law 
becomes  :  — 


which  holds  for  completely  dissociated  solutions,  where 
a  =  i,  and  also  for  solutions  in  which  the  dissociation  is 
not  complete. 

The  relation  between  the  migration  velocity  of  the  ions 
and  conductivity  is  thus  completely  accounted  for  by 
our  theory. 

The  Conductivity  of  Solutions.  —  The  conducting  power 
of  a  solution  is  evidently  closely  connected  with  its  dis- 
sociation, since  only  ions  carry  the  current.  We  can  then 
obtain  new  light  on  the  dissociation  of  solutions  by  study- 
ing their  conductivity. 

The  conductivity  of  any  conductor  of  electricity  is  the 
reciprocal  of  the  resistance  of  that  conductor.  The  resist- 
ance r,  from  Ohm's  law,  is  expressed  thus  :  — 


7T 

r=—, 
c 


1  Lehrb.  allg.  Chem.,  II,  p.  673. 


2 OS  ELECTROLYTIC   DISSOCIATION 

in  which  TT  is  the  difference  in  potential  at  the  two  ends  of 
the  conductor,  and  c  is  the  strength  of  current.  The  con- 
ductivity C  is  therefore :  — 

C  =  ~. 

7T 

The  unit  of  resistance  most  generally  used  is  that  of  a 
column  of  pure  mercury  106  cm.  in  length  and  I  sq.  mm. 
in  section,  at  o°  C. 

Specific  Conductivity.  —  The  resistance  of  conductors 
Depends  upon  their  form  as  well  as  upon  their  chemical 
nature.  In  order,  therefore,  that  the  resistances  of 
different  substances  may  be  measured  so  as  to  be  com- 
parable, it  is  necessary  that  the  conductors  should  have 
the  same  or  comparable  forms.  The  dimensions  usually 
chosen  are  a  cylinder  i  m.  in  length  and  i  sq.  mm.  in  sec- 
tion. The  resistance  offered  by  substances  of  these 
dimensions  is  known  as  their  specific  resistance. 

The  term  "specific  resistance"  is,  sometimes,  applied 
also  to  the  resistance  offered  by  a  cube  whose  edge  is 
i  cm.  in  length.  This  is  yoro  o"  of  ^e  f°rmer- 

The  term  "specific  resistance,"  or  its  reciprocal,  "spe- 
cific conductivity,"  can  be  applied  to  conductors  of  the 
second  as  well  as  to  those  of  the  first  class.  In  this  case, 
the  specific  conductivity  would  be  the  conductivity  of  a 
cylinder  of  the  liquid  i  m.  in  length  and  I  sq.  mm.  in 
cross-section. 

Conductors  of  the  second  class  are,  however,  generally 
solutions  of  some  electrolyte  in  some  solvent,  and  their  con- 
ductivity is  conditioned  by  the  presence  of  the  electrolyte. 
That  the  resistances  of  such  solutions  should  be  com- 
parable, it  is  clear  that  we  must  deal  with  comparable 


APPLICATIONS  OF  THE  THEORY  2O3 

quantities  of  the  dissolved  substances.  The  most  con- 
venient quantities  are  gram-molecular  weights  of  the 
different  substances. 

Given  a  normal  solution,  which  contains  a  gram-molecu- 
lar weight  of  the  electrolyte  in  a  litre.  Let  us  place  the 
litre  of  solution  between  two  electrodes  which  are  i  cm. 
apart.  The  cross-section  of  this  solution  would  be  1000 
sq.  cm. 

If  we  represent  by  v  the  number  of  cubic  centimetres 
of  any  solution  which  contains  #  gram-molecular  weight  of 
the  dissolved  substance,  and  by  jf  the  specific  conductivity 
of  a  cube  of  the  solution  whose  edge  is  i  cm.  in  length,  the 
molecular  conductivity,  p,  is  the  product  of  these  two  :  — 

fl  =  VS. 

But  rf  we  represent  by  s  the  specific  conductivity  of  a 
prism  of  the  solution,  i  m.  in  length  and  i  sq.  mm.  in  cross- 
section,  the  molecular  conductivity  is  expressed  thus  :  — 
/A=  loooovs. 

A  general  expression  for  the  molecular  conductivity, 
where  g  gram-molecular  weights  are  contained  in  a  litre  of 
the  solution,  is  :  — 


depending  upon  our  definition  of  specific  resistance, 
whether  it  is  referred  to  a  cube  of  the  solution  whose  edge 
is  i  cm.  long,  or  to  a  cylinder  of  it  I  m.  long  and  i  sq.  mm. 
in  cross-section. 

Method  of  Measuring  the  Conductivity  of  Solutions.  — 
If  a  continuous  current  is  passed  through  an  aqueous 
solution  of  an  electrolyte  from,  say,  platinum  '  electrodes, 


2O4 


ELECTROLYTIC   DISSOCIATION 


the  electrodes  will  become  covered  with  gas.  The  resist- 
ance of  the  solution  cannot  then  be  measured  as  such, 
since  this  polarization  of  the  electrodes  will  introduce  a 
new  source  of  resistance  into  the  circuit.  The  effect  of 
polarization  must  be  overcome  by  some  means.  Kohl- 
rausch  has  accomplished  this  by  using  an  alternating 
current.  His  method  consists  in  passing  an  alternating 
current  from  a  very  small  induction  coil  between  platinum 


plates  immersed  in  the  solution.  The  resistance  of  the 
solution  is  balanced  against  a  rheostat,  using  a  Wheatstone 
bridge  and  telephone.  A  dynamometer  may  be  used 
instead  of  the  telephone,  for  determining  the  reading  on 
the  bridge.  A  galvanometer  cannot,  of  course,  be  used 
with  an  alternating  current. 

The  Kohlrausch  apparatus  is  sketched  diagrammatically 
in  Fig.  8.  J  is  a  small  induction  coil,  tuned  to  a  very  high 
pitch,  and  should  be  placed  at  some  distance  from  the 


APPLICATIONS  OF  THE  THEORY  205 

bridge,  or  enclosed  in  a  box  lined  with  cotton,  to  deaden 
the  sound.  It  is  driven  by  a  storage  cell.  AB  is  a  metre 
stick  divided  accurately  into  millimetres.  Over  this  is 
stretched  a  wire  of  platinum,  or,  better,  of  manganine 
(an  alloy  containing  manganese)  or  nickelic,  which  have 
a  very  small  temperature  coefficient  of  resistance.  W  is  a 
rheostat.  R  is  the  vessel  containing  the  solution  and  elec- 
trodes. The  electrodes  are  cut  from  thick  sheet  platinum, 
and  into  each  plate  a  piece  of  stout  platinum  wire,  about  an 
inch  in  length,  is  welded.  The  wire  is  sealed  into  a  glass 
tube  which  is  filled  with  mercury,  and  electrical  connection 
thus  established  between  the  plate  and  the  copper  wire 
which  is  immersed  in  the  mercury.  One  arm  of  the  tele- 
phone T  is  thrown  into  the  circuit  between  the  rheostat 
and  the  resistance  vessel,  and  the  other  arm  is  connected 
with  the  bridge  wire  by  means  of  a  slider.  This  is  moved 
along  the  wire  until  that  point  is  found  at  which  the  hum 
of  the  induction  coil  ceases  to  be  audible  in  the  telephone. 
If  this  is  some  point  C,  and  we  represent  AC  by  a,  BC  by  &, 
the  resistance  in  W  by  w,  and  the  resistance  of  the  solu- 
tion in  the  vessel  by  r,  then  from  the  principle  of  the 

bridge  we  have :  — 

ra  —  wb, 

wb 
r  — 

a 

But  the  conductivity  of  a  solution  c  is  the  reciprocal  of  the 

resistance  r ;  therefore  :  — 

a 
wb 

The   conductivities   of   solutions   determined  from  this 
expression  would  not   be  comparable  with  one  another, 


2O6  ELECTROLYTIC  DISSOCIATION 

since  there  is  nothing  in  this  expression  which  takes  into 
account  the  concentration  of  the  solution.  It  is  most  con- 
venient to  refer  all  concentrations  to  molecular  normal, 
which  contains  a  gram-molecular  weight  of  the  electro- 
lyte in  a  litre.  If  we  represent  by  v  the  number  of  litres 
of  the  solution  which  contains  a  gram-molecular  weight 
of  the  electrolyte,  the  above  expression  becomes:  — 

c=™. 

wo 

Instead  of  c,  we  now  write  for  the  molecular  conduc- 
tivity the  letter  ft.  And  to  indicate  the  concentration  at 
which  the  p  is  determined,  we  write  /*„.- 

*  va 

*.-•» 

Even  this  expression  does  not  take  into  account  the 
dimensions  of  the  cell  used.  A  cell  constant  k  must  be 
introduced  and  determined  for  each  cell,  before  it  can  be.) 
employed  for  conductivity  measurements.  The  complete 
expression  for  calculating  the  molecular  conductivity  pv  is 
then :  — 

i  va 

^v  =  k  — 

wb 

Carrying  out  a  Conductivity  Measurement.  —  To  carry 
out  a  conductivity  measurement,  the  constant  k  for  the 
cell  must  first  be  determined.  For  this  purpose  a  solution 
must  be  used  whose  value  of  pv  is  known.  The  value  of 
ftp  for  a  one-fiftieth  normal  solution  of  potassium  chloride 
at  25°  is  129.7. 

The  platinum  plates  are  covered  with  platinum  black, 
by  electrolyzing,  in  the  cell,  a  dilute  solution  of  platinic 


APPLICATIONS  OF  THE  THEORY  207 

chloride.     The  —  solution  of  potassium  chloride  is  placed 

50 
in  the  cell,  the  latter  introduced  into  a  thermostat  which 

is  exactly  at  25°,  and  the  values  of  a,  b,  and  w  ascertained ; 
v  and  fjiv  are  known,  and  k  can  be  calculated  at  once. 

Having  determined  the  cell  constant,  the  measurement 
of  the  conductivity  of  a  solution  is  comparatively  simple. 
The  solution  of  known  concentration  is  placed  in  the  cell, 
warmed  accurately  to  the  temperature  desired,  and  then 
the  values  of  a,  b,  and  w  ascertained ;  k  and  v  being 
known,  pv  is  calculated  at  once. 

Conductivity  of  Water.  — The  conductivity  of  the  water 
used  is  very  important.  When  we  determine  the  conduc- 
tivity of  an  aqueous  solution,  what  we  actually  measure  is 
the  sum  of  the  conductivities  of  the  electrolyte  and  of 
the  water  used  in  preparing  the  solution.  For  this  reason 
very  pure  water  must  be  used  in  such  work,  and  a  number 
of  methods  for  purifying  water  for  conductivity  measure- 
ments have  been  devised. 

It  is  quite'  certain  that  perfectly  pure  water  has  never 
been  prepared.  The  purest  has  undoubtedly  been  obtained 
by  Kohlrausch  and  Heydweiller.1  They  distilled  in  a 
vacuum  the  purest  water  obtainable  by  other  methods,  and 
determined  its  conductivity  without  allowing  it  to  come  in 
contact  with  the  air.  A  millimetre  of  this  water,  at  zero 
degrees,  has  a  resistance  equal  to  that  of  a  copper  wire 
I  mm.  in  diameter,  extending  one  thousand  times  around 
the  earth. 

It  is,  of  course,  not  practicable  to  prepare  water  of  this 
degree  of  purity  for  ordinary  conductivity  measurements. 

1  Ztschr.  phys.  Chem.,  14,  317. 


208  ELECTROLYTIC  DISSOCIATION 

A  number  of  methods  are,  however,  available  for  purifying 
water  sufficiently  for  such  measurements. 

Nernst1  suggests  fractional  crystallization.  Hulett2  dis- 
tilled water  first  from  potassium  bichromate  and  sulphuric 
acid,  and  then  redistilled  it  from  a  solution  of  barium 
hydroxide. 

Jones  and  Mackay3  distilled  ordinary  distilled  water 
from  potassium  bichromate'  and  sulphuric  acid,  and  then 
passed  the  vapor  directly  into  a  boiling  alkaline  solution 
of  potassium  permanganate.  Two  distillations  were  thus 
effected  at  once. 

Any  of  the  above  methods  will  yield  water  of  sufficient 
purity  for  ordinary  conductivity  work. 

The  fact  that  pure  water  does  not  conduct  the  current, 
means  that  it  is  practically  undissociated.  This  same  fact 
has  been  shown  by  a  number  of  independent  investiga- 
tions, in  which  widely  different  methods  have  been  used. 
Space  will  not  permit  of  a  discussion  of  these  exceedingly 
interesting  pieces  of  work.  Reference  only,  can  be  made 
to  that  of  Wijs,4  Arrhenius,5  Ostwald,6  Bredig,7  Nernst,8 
and  Kohlrausch.9  The  reader  is  urgently  advised  to  care- 
fully examine  these  investigations,  which  all  agree  in 
showing  that  water  is  very  slightly  dissociated. 

The  fact  that  Water  is  undissociated  is  of  great  im- 
portance. It  means  that  hydrogen  and  hydroxyl  ions 
cannot  remain  in  the  presence  of  each  other  uncombined. 
This  has  already  been  referred  to  (p.  122),  in  connection 

1  Ztschr.  phys.  Chem.,  8,  120.  «  Ibid.,  n,  521. 

2  Ibid.,  21,  297.  7  Ibid.,  u,  829. 
8  Ibi'd.,  22,  237;  Amer.  Chem.  Journ.,  19,  91.  8  Ibid.,  14,  155. 
4  Ibid.,  ii,  492.  9  Ibid.,  14,  317. 
» Ibid.,  5,  16. 


APPLICATIONS  OF  THE  THEORY  2OQ 

with  the  explanation  of  the  phenomenon  of  neutralization 
of  acids  and  bases.  The  great  tendency  of  hydrogen  and 
hydroxyl  ions  to  unite  is,  undoubtedly,  the  conditioning 
cause  of  a  large  number  of  chemical  reactions.  This  will 
become  apparent,  when  we  recall  how  many  chemical  reac- 
tions there  are  in  which  a  molecule  of  water  is  formed. 

Calculation  of  Dissociation.  —  The  calculation  of  disso- 
ciation from  conductivity  is  comparatively  simple.  The 
molecular  conductivity  of  strong  acids  and  bases  and  salts 
increases  from  any  moderate  dilution  up  to  a  dilution  of 
about  1000  litres,  where  it  becomes  constant.  This  maxi- 
mum constant  value  of  the  molecular  conductivity  means 
complete  dissociation.  If  the  solution  is  not  dissociated  at 
all,  the  conductivity,  and,  consequently,  the  molecular  con- 
ductivity, is  zero.  To  calculate  the  dissociation  of  any 
partially  dissociated  solution,  it  is  only  necessary  to  deter- 
mine the  ratio  between  the  molecular  conductivity  of  the 
solution  in  question  and  the  molecular  conductivity  of  the 
substance  when  completely  dissociated. 

Representing  the  molecular  conductivity  of  the  solution 
of  volume  v  by  /*„,  and  the  molecular  conductivity  when 
the  substance  is  completely  dissociated  by  ^y  the  per- 
centage of  dissociation  a  is  calculated  thus  :  — 


The  value  of  /*„  for  any  dilution  of  any  substance  can 
be  ascertained  at  once  by  means  of  the  conductivity 
method.  The  value  of  /*«,  for  the  strongly  dissociated 
electrolytes  can  also  be  determined  directly  by  the  con- 
ductivity method.  It  is  only  necessary  to  increase  the 


210  ELECTROLYTIC   DISSOCIATION 

dilution  of  the  solution  until  the  molecular  conductivity 
attains  a  constant  maximum  value.  This  is  usually  reached 
at  about  1000  litres.  If  the  electrolyte  is  not  strongly 
dissociated,  as  in  the  case  of  the  organic  acids  and  bases, 
resort  must  be  had  to  an  indirect  method  of  determining 
the  value  of  p^.  This,  again,  can  only  be  referred  to,1 
since  space  will  not  allow  it  to  be  more  fully  discussed. 

It  will  be  seen  at  once  from  Kohlrausch's  law,  that  the 
conductivity  method  can  also  be  used  to  determine  the 
velocity  of  ions.  In  terms  of  this  law  the  value  of  /*«, 
for  any  compound,  is  the  sum  of  two  constants,  the  one 
depending  upon  the  anion,  and  the  other  upon  the  cation. 
These  constants  represent,  further,  the  relative  velocities 
of  the  two  ions. 

Given  a  compound  like  hydrochloric  acid ;  we  determine 
the  value  of  p^  for  the  compound,  by  the  conductivity 
method.  This  is  the  sum  of  the  velocities  of  the  hydrogen 
and  chlorine  ions.  We  know  the  velocity  of  the  hydro- 
gen ion.  If  we  subtract  this  from  the  value  of  /*„  for 
hydrochloric  acid,  we  obtain  the  velocity  of  the  chlorine 
ion. 

This  principle  has  been  used  extensively,  especially  by 
Ostwald2  and  Bredig,3  for  determining  the  relative  velocity 
of  ions.  The  work  of  Ostwald  is  typical.  He  wished 
to  determine  the  relative  velocities  of  the  anions  of  a 
number  of  organic  acids.  He  prepared  the  sodium  salts 
of  each  of  these  acids,  and  determined  the  value  of 
/*«  for. these  sodium  salts,  by  the  conductivity  method. 
The  value  of  /&„  for  the  sodium  salts  is,  from  Kohlrausch's 

1  Ostwald,  Lehrb.  d.  allg.  Chem.,  II,  p.  692. 

2  Ztschr.  phys.  Chem.,  2,  840.  3  Ibid. 


APPLICATIONS   OF  THE  THEORY  211 

law,  the  sum  of  the  velocities  of  the  sodium  cation  and 
of  the  organic  anion  of  the  acid.  Knowing  the  velocity 
of  sodium  to  be  44.5  in  terms  of  the  units  used,  he  had 
but  to  subtract  this  number  from  the  ^  for  the  acid,  to 
obtain  the  velocity  of  the  anion  of  the  acid. 

Bredig 1  worked  on  a  very  large  number  of  organic 
bases.  Here,  it  was  necessary  to  prepare  a  salt  of  the 
base  which  would  be  strongly  dissociated,  and  would  give 
the  value  of  /&„  at  moderate  dilutions.  If  the  hydro- 
chloric acid  salt  was  used,  the  velocity  of  chlorine  must 
be  subtracted  from  the  /*„  found,  and  the  difference 
would  be  the  velocity  of  the  organic  cation. 

It  is  thus  a  very  simple  matter  to  determine  the 
relative  velocities  of  cations  and  anions,  since  Kohlrausch 
discovered  the  law  to  which  these  conform. 

A  number  of  stoichiometric  relations  between  the  com- 
position and  constitution  of  ions,  and  their  velocities,  have 
been  pointed  out  by  Ostwald  and  Bredig.  In  general,  the 
more  complex  the  ion  the  slower  it  moves.  Isomeric 
anions  have  very  nearly  the  same  velocity,  while  con- 
stitution has  a  marked  influence  on  the  velocity  of  cations. 
The  effect  of  certain  atoms,  and  also  of  the  symmetry  of 
the  molecule,  have  been  worked  out  by  Bredig.2  For 
details  in  this  connection,  his  original  communication  must 
be  consulted. 

The  conductivity  of  solutions  in  the  different  solvents 
varies  very  greatly.  Solutions  in  water  were  thought  to 
have  the  greatest  conductivity,  until  it  was  recently 
shown  that  solutions  in  liquid  ammonia  conduct  better 
than  in  water.  This  fact  has  been  confirmed  by  Goodwin 

1  Loc.  cit.  2  Loc .  cit. 


212  ELECTROLYTIC  DISSOCIATION 

and  Thompson,  in  their  work  on  the  dielectric  constant 
of  liquid  ammonia.  Next  to  these  solvents,  in  dissociat- 
ing power,  come  formic  acid,  methyl  alcohol,  ethyl  alcohol, 
acetone,  and  finally  the  oils,  hydrocarbons,  and  ethereal 
salts.  When  substances  which  conduct  well  in  water  are 
dissolved  in  the  last-named  solvents,  the  solutions,  as  has 
already  been  mentioned,  show  very  little  conductivity,  and 
are,  therefore,  very  slightly  dissociated. 

The  dissociation  in  solvents  whose  solutions  conduct 
but  little  cannot  be  measured  accurately  by  the  con- 
ductivity method,  on  account  of  the  difficulty  of  deter- 
mining the  value  of  ^.  The  most  strongly  dissociated 
electrolytes  are  not  completely  dissociated  by  these  sol- 
vents, at  dilutions  which  come  within  the  range  of  the 
conductivity  method.  Thus,  it  is  impossible  to  determine 
the  value  of  /*„  for  any  substance  in  ethyl  alcohol,  by  the 
conductivity  method.  The  values  of  /*„,  for  any  dilution, 
can  be  determined  in  these  solvents  as  well  as  in  water. 
Some  assumption,  however,  must  be  made  in  calculating 
the  value  of  ^,  which  may  introduce  considerable  error. 

The  freezing-point  method  can  be  used  with  only  a  few 
solvents,  because  most  substances  freeze  at  temperatures 
which  are  too  far  removed  from  the  ordinary  to  secure 
accurate  measurements. 

The  boiling-point  method  is,  at  least  theoretically,  the 
freest  from  objections  in  such  cases,  and  could  be  used 
to  measure  dissociation,  if  the  experimental  difficulties 
could  be  overcome. 

This  has  been  accomplished,  in  part,  by  H.  C.  Jones.1 
He  has  devised  a  boiling-point  apparatus  which  diminishes 

1  Amer.  Chem.  Journ.,  19,  581. 


APPLICATIONS  OF  THE  THEORY  213 

some  of  the  sources  of  error  inherent  in  other  forms,  and 
he  has  applied  this  to  the  measurement  of  electrolytic 
dissociation  in  methyl  and  ethyl  alcohols.1  The  results 
obtained  are  fairly  satisfactory.  A  comparison  of  the  dis- 
sociation of  a  few  salts,  by  water,  methyl  alcohol,  and  ethyl 
alcohol,  taken  from  the  paper  of  Jones,  is  given  in  the 
following  table :  — 


SUBSTANCE 

DILUTION 
NORMAL 

DISSOCIATION 
IN  WATER 

DISSOCIATION 
IN  METHYL 
ALCOHOL 

DISSOCIATION 
IN  ETHYL 
ALCOHOL 

KI, 

O.I 

88% 

52% 

25% 

Nal, 

O.I 

84% 

60% 

33% 

NH4I, 

O.I 

50% 

KBr, 

O.I 

86% 

5°% 

NaBr, 

O.I 

86% 

60% 

24% 

NH4Br, 

O.2 

49% 

21% 

CH3COOK, 

O.I 

83% 

36% 

16% 

CH3COONa, 

O.I 

38% 

14% 

The  dissociation  in  methyl  alcohol  is  more  than  half  of 
that  in  water.  The  dissociation  in  ethyl  alcohol  is  less 
than  one-third  of  that  in  water. 

This  method  can  also  be  applied  to  the  investigation  of 
solutions  in  other  solvents. 

Thomson's  Theory.  —  Reference  has  already  been  made 
to  a  theory  proposed  by  J.  J.  Thomson,2  which  connects 
the  dissociating  power  of  solvents  with  their  dielectric  con- 
stants. This  theory  will  now  be  given,  in  Thomson's  own 
words.  "  If  we  take  the  view  that  the  forces  which  hold 
the  atoms  in  the  molecules  together  are  electrical  in  their 
origin,  it  is  evident  that  these  forces  will  be  very  much 
diminished  when  the  molecule  is  close  to  the  surface  of,  or 

1  Ztschr.  phys.  Chem.,  Jubelband,  van't  Hoff. 

2  Phil.  Mag.,  36,  320. 


214  ELECTROLYTIC  DISSOCIATION 

surrounded  by,  a  conductor,  or  a  substance  like  water,  pos- 
sessing a  very  large  specific  inductive  capacity  (dielectric 
constant). 

"Thus,  let  A,  B  represent  two  atoms  in  a  molecule, 
placed  near  a  conducting  sphere,  then  the  effect  of  the 

electricity  induced 
on  the  sphere  by 
A  will  be  repre- 
sented by  an  oppo- 
site charge  placed 
at  A',  the  image 
of  A  in  the  sphere. 
If  A  is  very  near 
the  surface  of  the 

sphere,    then    the 
FIG.  9. 

negative  charge  at 

Ar  will  be  very  nearly  equal  to  that  at  A.  Thus,  the 
effect  of  the  sphere  will  be  practically  to  neutralize  the 
electric  effects  of  A  ;  as  one  of  these  effects  is  to  hold 
the  atom  B  in  combination,  the  affinity  between  the  atoms 
A  and  B  will  be  almost  annulled  by  the  presence  of 
the  sphere.  Molecules  condensed  on  the  surface  of  the 
sphere  will  thus  be  practically  dissociated. 

"The  same  effect  would  be  produced,  if  the  molecules 
were  surrounded  by  a  substance  possessing  a  very  large 
specific  inductive  capacity.  Since  water  is  such  a  sub- 
stance, it  follows,  if  we  accept  the  view  that  the  forces 
between  the  atoms  are  electrical  in  their  origin,  that  when 
the  molecules  of  a  substance  are  in  aqueous  solution,  the 
forces  between  them  are  very  much  less  than  they  are 
when  the  molecule  is  free,  and  in  a  gaseous  state." 


APPLICATIONS   OF  THE  THEORY       .  215 

The  above  results  show  that  the  solvent  with  the  higher 
dielectric  constant  has  the  higher  dissociating  power,  but 
that  the  two  are  not  proportional  is  seen  by  comparing  the 
above  values  for  dissociation,  with  the  dielectric  constants 
of  these  three  solvents. 

DIELECTRIC  CONSTANT 

Water,  76  to  78 

Methyl  alcohol,  32.5  to  34 

Ethyl  alcohol,  25.7  to  26 

We  have  not  yet  sufficient  data  to  fairly  test  the  value 
of  Thomson's  theory.  It  is  so  beautiful  and  simple,  and 
is  such  a  welcome  application  of  the  theory  of  electrolytic 
dissociation,  that  we  are  inclined  to  hope  that  it  may  be  of 
wide-reaching  significance. 

Conductivity  at  Elevated  Temperatures.  —  We  have, 
thus  far,  dealt  with  the  conductivity  of  solutions  —  of  one 
substance  in  the  presence  of  another.  The  question  still 
remains :  Do  any  substances  conduct  by  undergoing  de- 
composition when  alone  ?  Pure  substances  conduct  with- 
out undergoing  decomposition,  such  as  the  metals,  carbon, 
etc.,  which  belong  to  conductors  of  the  first  class.  But 
substances  which  undergo  decomposition  when  they  con- 
duct are  called  conductors  of  the  second  class.  Do 
any  pure  homogeneous  substances  belong  to  the  second 
class  ? 

At  elevated  temperatures,  a  number  of  pure  substances 
are  known  to  conduct  like  conductors  of  the  second  class, 
or  electrolytes.  Substances  which  are  liquid  at  ordinary 
temperatures  do  not  conduct,  and  are,  therefore,  non- 
electrolytes. 

It  thus  seems  that  heat  acts,  to  a  certain  extent,  like 


2l6  ELECTROLYTIC   DISSOCIATION 

a  solvent,  converting  a  substance  which  does  not  conduct 
into  one  which  has  the  power  to  carry  the  current. 

Electromotive  Force.  —  The  theory  of  electrolytic  dis- 
sociation has  also  been  applied,  with  beautiful  results,  to 
the  problem  of  the  source  of  the  electromotive  force  in 
primary  cells.  This  could  properly  be  dealt  with  under 
the  head  of  electrochemistry,  but  is  so  distinctly  physical 
in  its  nature,  that  it  will  be  taken  up  as  an  example  of 
the  application  of  this  theory  to  physical  problems. 

Strength  of  Acids  and  Bases.  —  The  applications  of  the 
theory  of  electrolytic  dissociation,  described  in  this  sec- 
tion, we  owe  almost  entirely  to  Ostwald.  Reference  has 
already  been  made  to  his  extensive  investigations  of  the 
conducting  power  of  electrolytes,  and  especially  of  the 
organic  acids.  His  law  connecting  dissociation  with  dilu- 
tion has  already  been  deduced.  It  will  be  remembered 
that,  if  we  represent  the  percentage  of  dissociation  by  a, 
and  the  dilution  of  the  solution,  or  number  of  litres  which 
contains  a  gram-molecular  weight  of  the  electrolyte,  by  v, 
the  Ostwald  dilution  law  is  : 

o 

- —     .     =  constant. 


It  has  already  been  pointed  out,  that  this  law  does  not 
hold  for  the  strongly  dissociated  electrolytes,  the  strong 
acids  and  bases,  and  the  salts ;  but  does  apply  to  the 
more  weakly  dissociated  compounds,  such  as  the  organic 
acids  and  bases. 

Ostwald  has  shown  that  the  value  of  the  constant  for 
a  substance  is  a  characteristic  of  that  substance,  and  an 
expression  of  its  chemical  activity. 


APPLICATIONS  OF  THE  THEORY  2I/ 

The  constant  for  any  substance  is  determined  by  meas- 
uring the  conductivity  of  the  substance  at  several  dilutions, 

calculating  the  dissociation  from  these  measurements,  by 

i/, 
means  of  the  formula  a  =  -^,    already    considered ;    and 

knowing  a  and  v,  the  constant  c  is  calculated  from  the 
Ostwald  dilution  law,  just  given.  An  example,  taken 
from  the  work  of  Ostwald,1  will  make  this  clear. 

FORMIC  ACID  (HCOOH).     ^  =  376 

V 

8 

16 

32 

64 
128 
256 

512  IO2.I  27.IO  O.OI97 

1024  134.7  35.80  0.0195 

The  constants  of  other  acids  and  bases  were  deter- 
mined in  exactly  the  same  manner.  In  this  investigation, 
Ostwald  studied  between  two  and  three  hundred  organic 
acids,  and  brought  out  some  interesting  and  important  facts 
in  connection  with  the  strength  of  these  acids,  and  pointed 
out  certain  relations  between  the  strength  of  the  acids  and 
their  composition  and  constitution. 

In  the  preceding  chapter,  it  was  shown  that  the  strength 
of  acids  thus  determined  by  conductivity,  agreed  with 
that  found  by  other  methods,  such  as  the  velocity  with 
which  they  inverted  cane-sugar,  saponified  methyl  acetate, 

1  Ztschr.  phys.  Chem.,  3,  170,  241,  369. 


/*« 

a 

cx  100 

15.22 

4-05 

0.0214 

21.19 

6.63 

0.0210 

29.31 

7-79 

O.O2O6 

40.50 

10.78 

O.O2O3 

55-54 

14.76 

O.O2OO 

75.66 

2O.  I  2 

0.0198 

2l8  ELECTROLYTIC  DISSOCIATION 

etc.  We  can,  then,  regard  conductivity  as  the  true  meas- 
ure of  the  strength  of  acids. 

But  conductivity  is  proportional  to  dissociation,  since  only 
ions  conduct  the  current.  Therefore,  the  strength  of  an 
acid  is  conditioned  by  the  amount  to  which  it  is  dissociated. 

All  acids  dissociate  into  a  hydrogen  cation,  and  into  the 
remainder  of  the  molecule  which  forms  the  anion.  The 
anion  may  be  simple,  consisting  of  the  halogen  alone,  as 
with  the  halogen  acids,  or  it  may  be  very  complex,  as  with 
the  higher  members  of  the  homologous  series  of  organic 
acids.  The  anion  differs  in  its  nature  with  every  acid. 
The  cation  of  all  acids,  however,  is  hydrogen,  and,  there- 
fore, the  acidity  of  these  compounds  is  due  to  this  common 
constituent  into  which  all  acids  dissociate. 

The  strength  of  acids,  then,  resolves  itself  into  the  num- 
ber of  hydrogen  ions  present  in  their  solutions.  When 
we  say  an  acid  is  strong,  we  mean  that  it  is  largely  dis- 
sociated in  solution,  or  that  its  solution  contains  a  large 
number  of  hydrogen  ions.  And  this  leads  us  to  an  inter- 
esting conclusion  pointed  out  by  Ostwald.  All  acids  are 
completely  dissociated  at  infinite  dilution ;  therefore,  at 
infinite  dilution  all  acids  have  the  same  strength.  Exactly 
the  same  remarks  apply  to  bases.  Bases  dissociate  into  a 
hydroxyl  anion,  and  the  remainder  of  the  compound  forms 
the  cation.  The  latter  may  be  simple,  as  with  the  alkalies, 
or  may  be  very  complex,  as  in  the  organic  bases. 

The  common  constituent  of  bases  is,  then,  the  hydroxyl 
anion,  and  basicity  is  due  to  the  presence  of  this  ion.  A 
strong  base  means  one  which  is  largely  dissociated,  or 
in  whose  solution  there  is  a  large  number  of  hydroxyl 
ions.  But  all  bases,  like  all  acids,  are  completely  disso- 


APPLICATIONS  OF  THE  THEORY  2IQ 

ciated  at  infinite  dilution.  Therefore,  all  bases  have  the 
same  strength  at  infinite  dilution. 

These  generalizations  for  acids  and  bases  are  of  very 
wide  significance,  and  greatly  simplify  and  correlate  phe- 
nomena, which  have  been  hitherto  regarded  as  more  or 
less  disconnected. 

Relations  between  Acidity  and  Composition  and  Constitu- 
tion. —  Some  of  the  relations  between  acidity  and  com- 
position and  constitution  will  be  considered. 

Hydrochloric,  hydrobromic,  and  hydriodic  acids  are  to 
be  ranked  among  the  strongest  acids.  They  have  very 
nearly  the  same  strength,  as  is  shown  by  the  fact  that  they 
conduct  to  just  about  the  same  extent.  Hydrofluoric  acid 
is  much  weaker,  as  is  shown  by  its  comparatively  small 
conductivity.  These  facts  are  established  by  the  following 
results:-  HQ  HBr  ffl  HF 


2 

33i 

34i 

34i 

— 

4 

343 

354 

353 

27.8 

8 

355 

361 

360 

33-6 

32 

369 

373 

372 

SS-8 

4096 

376 

372 

373 

— 

Hydrocyanic  acid  conducts  but  little  better  than  pure 
water,  and  is,  therefore,  one  of  the  weakest  acids.  When 
sulphur  is  introduced  into  this  acid,  we  have,  in  sulpho- 
cyanic,  one  of  the  strongest  acids. 

HCN  HCNS 

»  Mt>  /*t> 

2  326 

4  0.33  337 

8  0.38 

32  0.46  358 


220  ELECTROLYTIC  DISSOCIATION 

Hydrocyanic  acid,  judged  by  its  conductivity,  can,  there 
fore,  scarcely  be  regarded  as  an  acid,  while  sulphocyanic 
acid  is  nearly  as  strong  as  hydrochloric  acid. 

The  introduction  of  oxygen  usually  increases  the  acidity, 
that  is  to  say,  forms  a  compound  which  is  more  dissociated 
by  the  solvent.  This  is  by  no  means  general.  Take  the 
acids  of  phosphorus;  the  more  oxygen  there  is  present 
the  weaker  the  acid,  as  is  seen  in  the  following  results  :  — 

H8P02  H2P08  H3P04 

V  ft,  Hv  fr 

2  131          ,  121  60 

8  194  175  9° 

64     293     274     183 
256     330     316     262 

1024  344  336  320 

The  order  of  strength  of  some  of  the  more  common 
mineral  acids  is  as  follows,  expressed  in  terms  of  hydro- 
chloric acid  =  100  :  — 

HC1  100  HBr  101 

HN03  99.6  HI  92 

65.1  H3PO4  17 


Turning  to  the  organic  acids,  we  find  a  number  of  rela- 
tions established.  The  introduction  of  chlorine  into  the 
fatty  acids  increases  the  acidity.  Take  the  chlorine  sub- 
stitution products  of  acetic  acid  :  — 


CH3COOH 

CHjClCOOH 

CHC12COOH 

CClgCOOH 

V 

/*» 

P* 

Vv 

A*» 

2 

— 

21.2 

109 

245 

32 

8.65 

73-4 

256 

327 

128 

16.99 

126.0 

308 

336 

IO24 

46.00 

236.0 

342 

339 

APPLICATIONS   OF  THE  THEORY 


221 


The  introduction  of  oxygen  into  an  acid,  forming  the 
hydroxyl  group,  increases  the  acidity.  This  is  seen  from 
the  following  example  :  — 


2 

32 
64 

5" 
4096 


SUCCINIC  ACID 
C2H4(COOH), 

to 

3-73 


22.1 

58.6 

142.0 


MALIC  ACID 
C2H3(OH)(COOH)2 

8-45 
26.6 
50.8 
126.0 


TARTARIC  ACID 
C2H2(OH)2(COOH)a 


58.1 

79-4 
183.0 
341.0 


The  effect  of  introducing  one  and  two  hydroxyl  groups 
is  shown  in  these  examples. 

In  the  aromatic  series  we  have  to  take  into  account  not 
simply  the  nature  of  the  group,  but  the  position  which  it 
takes,  whether  ortho,  meta,  or  para.  The  introduction  of 
oxygen  into  benzoic  acid,  forming  a  hydroxy  acid,  has  a 
very  different  influence  on  the  acidity,  depending  upon  the 
position  occupied  by  the  oxygen. 

BENZOIC  ACID         SALICYLIC  ACID         ^/-OXYBENZOIC  P-OXYBENZOIC 

(o)  ACID  ACID 

C6H4(OH)COOH      C6H4(OH)COOH  C6H4(OH)COOH 
to  to 


C6H5COOH 

C6H4(OH)C 

V 

to 

to 

64 

22.1 

8l.2 

256 

42.3 

137-0 

2048 

104.0 

255-0 

25-5 

47-7 
114.0 


14-3 
28.3 

73-0 


Hydroxyl  in  the  ortho  position  increases  the  acidity  very 
markedly.  In  the  meta  position  it  has  but  a  slight  effect, 
while  in  the  para  position  it  actually  lessens  the  acidity. 

The  introduction  of  the  nitro  group  has  a  very  different 
influence,  depending  upon  its  position. 


V 

/*« 

Mv 

64 

22.1 

*59 

512 

57-9 

263 

2048 

104.0 

301 

222  ELECTROLYTIC  DISSOCIATION 

BENZOIC  ACID      O-NITROBENZOIC       ^/-NITROBENZOIC      P-NITROBENZOIC 
ACID  ACID  ACID 

47-5 

II7.0  123 

190.0  195 

The  nitro  group  in  the  ortho  position  has  the  greatest 
acidifying  power,  while  in  the  para  position  it  has  some- 
what greater  power  than  in  the  meta. 

The  introduction  of  more  and  more  nitro  groups,  in 
general,  increases  the  acidity.  Thus,  take  phenol,  which 
is  a  very  weak  acid.  Introduce  one  nitro  group,  we  have 
its  acidity  increased.  Introduce  a  second  nitro  group, 
and  its  acidity  is  still  further  increased.  Introduce  the 
third  nitro  group,  and  we  have  picric  acid,  which  is  nearly 
as  strong  as  the  mineral  acids. 

As  the  unsaturated  acids  contain  less  and  less  hydro- 
gen, the  affinity  increases.  Thus,  acrylic  acid,  C3H4O2,  is 
stronger  than  propionic,  C3H6O2.  The  effect  of  constitu- 
tion can  be  seen  by  studying  the  acidity  of  maleic  and 
fumaric  acids,  which  have  the  same  composition. 

MALEIC  ACID  FUMARIC  ACID 

V  tin  Wt; 

32  166  58.8 

512  305  179.0 

2048  338  275.0 

8192  339  337.0 

Maleic  is  much  stronger  for  the  greater  concentrations, 
but  never  has  a  molecular  conductivity  greater  than  a 
monobasic  acid.  Fumaric,  at  high  dilution,  has  a  greater 
conductivity  than  a  monobasic  acid.  The  second  hydro- 


APPLICATIONS  OF  THE  THEORY  223 

gen  takes  part   in  the  conductivity,  before  the  first  has 
reached  a  maximum. 

Take  citraconic  acid  and  two  of  its  isomeres :  — 

CITRACONIC  ITACONIC  MESACONIC 


V 

f*v 

f^v 

Mw 

8 

56-4 

11.7 

25.5 

512 

250.0 

84.7 

162.0 

4096 

322.0 

186.0 

291.0 

From  its  conductivity,  citraconic  acts  like  a  monobasic 
acid.  In  itaconic  one  carboxyl  is  weaker  than  the  other, 
while  mesaconic  conducts  itself  like  a  dibasic  acid,  whose 
hydrogen  atoms  are  nearly  or  quite  equivalent.  By  a 
careful  study  of  the  conductivity  of  acids,  as  Ostwald  has 
shown,  some  light  can  be  thrown  on  their  constitution. 

The  introduction  of  the  amido  group  weakens  the  acid 
properties,  as  would  be  expected  from  the  basic  nature 
of  this  group. 

Bases.  —  Some  work  has  been  done  on  strength  of  bases 
by  Ostwald,1  Bredig,2  and  others.  But  these  have  not 
been  worked  up  as  thoroughly  as  the  organic  acids. 

The  conductivities  of  the  strong  bases,  like  those  of 
the  strong  acids,  reach  a  maximum  at  a  dilution  of  about 
one  thousand  litres.  The  value  of  /*„  for  the  bases  is 
less  than  for  the  acids,  since  the  velocity  of  the  hydroxyl 
ion  is  only  about  170,  while  the  velocity  of  the  hydrogen 
ion  is  about  325  at  25°C.  The  strong  bases  include  the 
hydroxides  of  the  alkalies  and  alkaline  earths.  Ammonia 
is  sometimes  regarded  as  a  strong  base,  but  it  is  not 

1  Journ.  prakt.  Chem.  (2),  33,  352. 

2  Ztchr.  phys.  Chem.,  13,  289. 


224  ELECTROLYTIC  DISSOCIATION 

It  was  found  that  the  conductivity  of  ammonia  is  slight, 
compared  with  that  of,  say,  potassium  hydroxide.  Other 
reactions  with  ammonia  were  also  studied,  such  as  the 
velocity  with  which  it  would  effect  reactions,  and  these 
results  confirmed  those  from  conductivity.  Ammonia  is, 
then,  a  comparatively  weak  base. 

We  will  now  compare  the  strength  of  ammonia  with 
that  of  the  substituted  ammonias:  — 

NH3  NH2CH3          NH2C2H6       NH2C3H7       NH2C4H9 

*V  //•»  At*  M*  M»  IJLj 


2 

I.46 

6.41 

6.06 



— 

32 

6.13 

26.4 

26.8 

23-7 

19-5 

256 

I7.8 

64.8 

66.9 

59-2 

49.2 

IO24 

37-0 

I08.0 

II2.O 

97-7 

82.3 

Thus,  all  monamines  are  stronger  than  ammonia. 
We  will  examine  some  of  the  di-  and  triamines. 

NH(CH3)2        NH(C2H6)2  N(CH8)S  N(C2H6)3 

*V  Mt »  fJ*n  MB  A&M 

2  6.88  2.63  4.76 

128  55.9  65.8  23.7  49.7 

1024  120.7  I3°-3  56*8  n. 6 

Dimethylamine  is  only  a  little  stronger  than  methyl- 
amine,  and,  similarly,  diethylamine  is  but  little  stronger 
than  ethylamine. 

The  triamines  are  not  as  strong  as  the  diamines.     The 
results  for  one  of  the  tetramines  are  given :  — 

(C2H6)4NOH 
v  fa 

16  176.2 

128  186.4 

1024  182.6 


APPLICATIONS  OF  THE  THEORY  225 

and  these  show  that  the  compound  is  a  fairly  strong  base ; 
indeed,  much  stronger  than  either  of  the  other  amines. 

The  effect  of  introducing  two  amido  groups  into  a 
compound  can  be  seen  from  ethylene  diamine. 

C2H4(NH2), 

V  •     Hv 

32  8.90 

256  23.16 

1024  40.91 

It  is  surprising  that  the  ethylene  diamine  is  much 
weaker  than  the  ethylamine,  since  two  amido  groups 
should  increase  the  basic  property.  This  suggests  the 
acids  of  phosphorus,  where  the  weaker  acid  is  the  one 
containing  the  greater  number  of  oxygen  atoms. 

A  large  number  of  relations  between  composition  and 
constitution  and  chemical  activity  have  been  worked  out, 
but  those  already  given  suffice  to  show  the  nature  of  the 
relations  which  have  been  discovered.  No  generalization 
of  very  wide  significance  has  been  reached,  and  exceptions 
are  usually  present  to  any  general  statement  which  may 
be  made.  This  work  resembles,  in  many  respects,  the 
earlier  physical  chemical  investigations,  which  had  to  do 
with  problems  of  this  same  general  type. 

Although  many  exceptions  appear  in  work  of  this  kind, 
nevertheless,  its  value  is  great,  since  it  is  only  step  by  step 
that  we  arrive  at  the  truth,  and  a  great  many  steps  are 
required  to  arrive  at  truth  in  its  broader  relations.  We 
will  leave  here  the  chemical  side  of  modern  physical 
chemistry,  and  turn  to  the  application  of  the  theory  of 
electrolytic  dissociation  to  a  physical  problem, 

Q       ' 


226  ELECTROLYTIC  DISSOCIATION 

APPLICATION    OF   THE    THEORY    OF    ELECTROLYTIC    DISSOCIA- 
TION   TO   A    PHYSICAL    PROBLEM 

The  theory  of  electrolytic  dissociation  has  not  been 
applied  as  widely  to  physics  as  it  has  been  to  chemistry. 
This,  from  the  nature  of  the  case,  was  to  be  expected. 
Ions  are  the  main,  if  not  the  sole  factors  in  chemical 
activity;  while  molecules  are  generally  the  units  with 
which  the  physicist  has  to  deal. 

That  chapter  of  physics,  which  is  most  concerned  with 
ions,  is  the  one  which  has  to  do  with  electrical  phenomena, 
and,  especially,  with  electricity  as  generated  in  primary 
cells.  Here,  one  of  the  essential  agents  is  a  solution  of 
some  electrolyte,  or  solutions  of  more  than  one  electrolyte, 
and  these  solutions  are  always  more  or  less  dissociated. 
The  ions  are,  thus,  essential  to  the  action  of  such  cells,  and 
here  our  theory  bears  directly  upon  a  problem  which  is, 
indeed,  a  physical  one. 

THE   SEAT   OF   THE   ELECTROMOTIVE   FORCE   IN   PRIMARY 

CELLS 

The  question  as  to  the  origin  of  the  electromotive  force 
in  primary  cells  is  as  old  as  the  cell  itself.  Volta  con- 
cluded that  the  main  source  of  the  electromotive  force  was 
at  the  point  of  contact  of  the  two  metals.  Others  have 
supposed  that  the  contact  of  the  two  solutions  was  the 
chief  source  of  the  electromotive  force.  Others,  again, 
sought  for  the  electromotive  force  of  such  elements,  at  the 
points  of  contact  of  the  electrodes  with  the  electrolytes. 
The  question  was  unsettled  when  the  theory  of  electro- 
lytic dissociation  was  proposed.  We  shall  see  that  this 


APPLICATIONS  OF  THE  THEORY  22? 

theory  has  furnished  us  with  a  solution  to  this  problem, 
and  we  now  have  a  pretty  clear  conception  of  what  takes 
place  in  the  primary  cell. 

The  application  of  the  van't  Hoff  laws  of  osmotic  press- 
ure, and  the  Arrhenius  theory  of  electrolytic  dissociation, 
to  explain  the  action  of  the  cell,  we  owe  to  Nernst,1  who 
did  this  epoch-making  work  while  in  the  laboratory  of 
Ostwald  in  Leipzig. 

It  will  be  assumed  that  the  reader  is  familiar  with  the 
method  of  measuring  the  electromotive  force  of  elements. 
The  method,  in  general,  is  to  balance  the  cell  in  ques- 
tion against  one  of  standard  electromotive  force,  such 
as  the  Clarke  element,  by  means  of  a  convenient  resistance 
box,  and  using  the  Lippmann  electrometer  to  determine 
the  point  of  equilibrium.  We  will  not  spend  more  time 
upon  this  experimental  side  of  the  problem,  but  proceed 
at  once  to  the  calculation  of  the  electromotive  force  of 
elements. 

Calculation  of  Electromotive  Force  from  Osmotic  Press- 
ure. —  The  method  of  calculating  electromotive  force 
from  osmotic  pressure  is  given  essentially  as  deduced  by 
Ostwald2  from  the  work  of  Nernst. 

If  we  allow  a  substance  to  pass,  isothermally,  from 
one  condition  to  another,  the  maximum  amount  of  ex- 
ternal work  is  always  the  same,  regardless  of  how  this 
takes  place,  whether  osmotically,  or  electrically,  or  in  any 
other  way.  If  we  know  the  maximum  external  work 
which  is  obtainable  from  a  process,  we  know  the  amount 
of  electrical  energy;  and,  as  we  shall  see,  the  electro- 
motive force  is  calculated  directly  from  the  electrical 

1  Ztschr.  phys.  Chem.,  4,  129.  2  Lehr.  d.  allg.  Chem.,  II,  p.  825. 


228  ELECTROLYTIC   DISSOCIATION 

energy.  The  first  step  is,  then,  to  determine  the  maximum 
external  work  which  is  obtainable  in  a  given  process. 
This  can  be  done  by  allowing  the  substance  to  pass,  at 
constant  temperature,  in  a  reversible  manner,  from  one 
condition  over  to  the  other. 

Given  a  gas  under  a  pressure  /1?  and  volume  v,  and 
allow  it  to  expand  isothermally  to  a  pressure  /2.  When  a 
gas  expands  isothermally  it  takes  up  heat,  and  gives  it  up 
as  volume  energy.  The  energy  set  free  under  these  con- 
ditions is  :  — 

A 

—  Cvdp. 
Pi 

But  pv  =  RT,  where  R  is  the  gas  constant  and  T  the 
absolute  temperature,  whence  the  above  expression  be- 
comes for  gram-molecular  weights  :  — 


Pi 

which  expresses  the  volume  energy  obtained  under  the 
condition. 

This  becomes  on  integration  :  — 


A 

This  amount  of  energy,  which  is  converted  into  work  by 
an  ideal  gas  in  passing  from  pressure  p^  to  pressure  /2,  is 
exactly  equal  to  the  work  obtained  from  an  ideal  solution 

*  In  is  natural  logarithm. 


APPLICATIONS  OF  THE  THEORY  229 

under  the  same  conditions.  That  is,  a  solution  ol  volume 
v  passing,  isothermally,  from  an  osmotic  pressure  /x  to  an 
osmotic  pressure /2. 

But  with  the  movements  of  the  ions,  we  have  the  move- 
ments of  the  electrical  charges  which  they  carry.  And, 
from  what  has  been  said,  the  amounts  of  work  correspond- 
ing to  the  movements  of  the  ions  can  be  transformed  into 
electrical  energy. 

We  have,  then,  shown,  thus  far,  how  to  calculate  the 
maximum  external  work  obtainable,  when  a  solution  of 
osmotic  pressure  /x  passes  isothermally  and  reversibly 
over  to  osmotic  pressure  /2,  and  the  relation  between  this 
work  and  the  electrical  energy  obtainable. 

But  knowing  the  electrical  energy,  how  can  we  deter- 
mine the  electromotive  force  ?  Electrical  energy,  like  every 
other  manifestation  of  energy,  can  be  factored  into  an 
intensity  and  a  capacity  factor.  The  intensity  factor  of 
electrical  energy  is  the  electromotive  force,  or  potential, 
and  the  capacity  factor  the  amount  of  electricity.  If  we 
call  the  former  TT,  and  the  latter  eQ,  we  have  the  energy 
electric  ee  =  7reQ.  If  we  know  e&  we  can  calculate  TT  at 
once,  since  eQ  is  known  from  Faraday's  law.  Knowing 
the  quantity  of  ions  which  pass  from  one  osmotic  pressure 
over  to  the  other,  we  know  the  amount  of  electricity  eQ ; 
knowing  ee,  we  calculate  TT. 

Let  us  deal  with  a  gram-molecular  weight  of  univalent 
ions.  These  will  carry  96,540  coulombs  of  electricity,  and 
this  quantity  we  will  now  designate  by  eQ.  If  the  ions  are 
bivalent  they  will  carry  twice  as  much ;  if  trivalent  three 
times,  and  so  on.  Let  us  represent  the  valence  of  the 
ions  by  v ;  then  a  gram-molecular  weight  will  carry  ve§ 


230  ELECTROLYTIC  DISSOCIATION 

amount  of  electricity.  Suppose  a  gram-molecular  weight 
of  these  ions  is  charged  TT  potential.  The  amount  of 
electrical  energy  required  to  effect  this  charge  is  :  — 


But  this  electrical  energy  is  equal  to  the  osmotic,  calcu- 
lated above,  where  a  gram-molecular  weight  was  taken 
into  account.  We  have:  — 

=  R  T  In  —  ,  or 

A 


" — JT**' 

This  is  the  fundamental  equation  for  calculating  the 
electromotive  force  of  elements,  from  the  osmotic  pressures 
of  the  electrolytes  around  the  electrodes. 

This  equation  has  been  very  much  simplified  by 
Ostwald,1  by  introducing  numerical  values  wherever  it 
is  possible. 

R  =  2  calories,  and  I  calorie  =  4.18  x  io7  ergs.  7",  the 
absolute  temperature,  can  be  taken  as  29O°C.  for  the  aver- 

r>  y 

age   conditions.     The   constant  -   —  =  0.0251    volt,   since 

volt  x  coul  =  io7  ergs. 

The  above  equation  then  becomes :  — 

0.0251.    /t 
TT  = —  In  °» 

or  in  case  the  ions  are  univalent :  — 

77  =  0.0251  m^- 

1  Lehrb.  d.  allg.  Chem.,  II,  p.  827. 


APPLICATIONS   OF  THE  THEORY  231 

Thus  far  we  have  been  using  the  natural  logarithm 
obtained  in  the  process  of  integration,  which  we  have  writ- 
ten In.  It  is  far  more  convenient  in  practice  to  use  the 
Briggsian.  To  pass  from  the  former  to  the  latter  we  must 
divide  the  above  constant  by  0.4343,  when  we  obtain 
0.058. 

The  final  expression  of  the  general  formula  for  calcu- 
lating the  electromotive  force  of  an  element,  from  the 
osmotic  pressure  of  the  electrolytes  around  the  electrodes, 
is  then :  — 

77  =  0.058  log— » 
Ft 

where  log  is  the  Briggsian  logarithm.  If  the  valence  of 
the  ion  is  greater  than  one,  this  must  be  divided  by  the 
valence.  Before  attempting  to  apply  this  expression  to 
any  concrete  cases,  we  must  examine  another  conception 
introduced  by  Nernst. 

Electrolytic  Solution-tension. — We  are  perfectly  famil- 
iar with  the  fact  that  when  a  solid  or  liquid  is  evaporated, 
the  molecules  pass  into  the  space  above  the  liquid ;  and 
equilibrium  is  established,  for  a  given  temperature,  when 
the  vapor  exerts  a  certain  definite  pressure.  This  press- 
ure is  designated  as  the  vapor-tension,  or  vapor-pressure, 
of  the  substance  in  question. 

Says  Nernst : :  "  If,  in  accordance  with  van't  HofF s 
theory,  we  assume  that  the  molecules  of  a  substance  in 
solution  exist  also  under  a  definite  pressure,  we  must  ascribe 
to  a  dissolving  substance  in  contact  with  a  solvent,  simi- 
larly, a  power  of  expansion,  for  here,  also,  the  molecules 
are  driven  into  a  space,  in  which  they  exist  under  a  certain 

1  Ztschr.  phys.  Chem.,  4,  150. 


232  ELECTROLYTIC  DISSOCIATION 

pressure.  It  is  evident  that  every  substance  will  pass  into 
solution  until  the  osmotic  partial  pressure  of  the  molecules 
in  the  solution  is  equal  to  the  'solution-tension'  of  the 
substance." 

Nernst  thus  introduced  the  conception  of  solution-ten- 
sion ;  and,  at  the  same  time,  called  attention  to  the  close 
analogy  between  evaporation  and  solution,  which  can  be 
seen  only  through  a  knowledge  of  the  osmotic  pressure  of 
solutions.  The  metals,  like  many  other  substances,  have 
the  possibility  of  passing  into  solution  as  ions.  Every 
metal,  in  water,  has,  then,  a  certain  solution-tension  pecul- 
iar to  itself,  and  we  will  designate  this  by  P. 

If  we  dip  a  metal  into  pure  water,  let  us  see  what  will 
take  place.  In  consequence  of  the  solution-tension  of  the 
metal,  some  ions  will  pass  into  solution.  When  metallic 
atoms  pass  over  into  ions,  they  must  secure  positive  electric- 
ity from  something.  They  take  it  from  the  metal  itself, 
which  thus  becomes  negative.  The  solution  becomes 
positive,  because  of  the  positive  ions  which  it  has  received. 
At  the  plane  of  contact  of  the  metal  and  solution,  there  is 
formed  the  so-called  electrical  double  layer,  whose  exist- 
ence was  much  earlier  recognized  by  Helmholtz.1  The 
positively  charged  ions  in  the  solution  and  the  negatively 
charged  metal  attract  one  another,  and  a  difference  in 
potential  arises.  The  solution-tension  of  the  metal  tends 
to  force  more  ions  into  solution,  while  the  electrostatic 
attraction  of  the  double  layer  is  in  opposition  to  this. 
Equilibrium  is  established  when  these  two  forces  are 
equal.  Since  the  ions  carry  such  enormous  charges,  the 
number  which  will  pass  into  solution  before  equilibrium  is 

l  Wied,  Ann..  7,  337  (1879). 


APPLICATIONS  OF  THE  THEORY  233 

established  is  so  small  that  they  cannot  be  detected  by 
any  ordinary  method.  When  we  are  dealing  with  a  metal 
immersed  in  pure  water,  it  is  evident  that  the  difference  in 
potential  which  obtains  in  the  double  layer  is  conditioned 
only  by  the  magnitude  of  the  solution-tension  of  the  metal 
in  question. 

If  we  dip  a  metal  of  solution-tension  P,  into  a  solution 
of  one  of  its  salts,  the  case  is  not  quite  as  simple.  Let 
the  osmotic  pressure  of  the  metallic  ions  in  the  solution 
of  the  salt  be  /,  then  either  of  three  conditions  may  exist. 
Th£  solution-tension  may  be  greater  than  the  osmotic 
pressure,  less  than  the  osmotic  pressure,  or  just  equal  to  it. 
We  may  have  :  — 


P<P.  (2) 

P=P-  (3) 

Let  us  first  take  case  No.  i,  where  a  metal  of  solution- 
tension  P  is  immersed  in  a  solution  of  one  of  its  salts,  in 
which  the  osmotic  pressure  /  of  the  metallic  ions  is  less 
than  its  own  solution-tension. 

At  the  moment  the  metal  touches  the  solution,  a  number 
of  metallic  ions,  which  always  carry  a  positive  charge,  will 
pass  into  solution.  These  ions  have  carried  positive  elec- 
tricity from  the  metal  into  the  solution,  and  the  metal 
has  thus  become  negative,  the  solution  positive.  At  the 
places  where  the  metal  and  solution  come  in  contact,  the 
double  layer  is  formed,  due  to  the  attraction  of  the  opposite 
charges. 

"This  double  layer  has  a  component  of  force,  which 
acts  at  right  angles  to  the  plane  of  contact  of  the  metal 


234  ELECTROLYTIC  DISSOCIATION 

and  solution,  and  tends  to  drive  back  the  metallic  ions  from 
the  electrolytes  to  the  metal.  It  acts  in  direct  opposition 
to  the  electrolytic  solution-tension."  l 

The  condition  of  equilibrium  is  reached  when  these  two 
opposing  forces  just  equalize  one  another;  and  the  final 
result  is  the  existence  of  an  electromotive  force  between 
the  metal  and  the  solution,  the  metal  being  negative,  the 
solution  positive. 

It  is  clear  that  a  metal  cannot  throw  as  many  ions  into 
a  solution  of  its  salt,  as  into  pure  water,  because  the 
osmotic  pressure  of  the  metallic  ions  already  in  the  solu- 
tion acts  against  the  solution-tension  of  the  metal. 

Let  us  now  take  the  second  case ;  where  the  solution- 
tension  of  the  metal  is  less  than  the  osmotic  pressure  of 
the  metallic  ions  in  the  solution.  Metallic  ions  will  separate 
from  the  solution  upon  the  metal.  When  a  metallic  ion 
passes  over  into  an  atom  it  gives  up  its  positive  charge, 
and  in  this  case  it  gives  it  up  to  the  metal,  which  becomes 
positive.  The  solution,  having  lost  some  of  its  positively 
charged  ions,  becomes  negative.  At  the  points  of  contact 
of  solution  and  metal,  we  have  again  the  electrical  double 
layer,  but  this  time  the  metal  is  positive  and  the  solution 
negative,  which  is  exactly  the  reverse  of  the  case  first  con- 
sidered. Metal  ions  will  separate  from  the  solution  until 
the  electrostatic  component  of  force  of  the  double  layer,  at 
right  angles  to  the  plane  of  contact  of  metal  and  solution, 
is  just  equal  to  the  excess  of  the  osmotic  pressure  over  the 
solution-tension.  Equilibrium  is  established  when  the  sum 
of  the  solution-tension  of  the  metal  and  this  component  of 
force  is  just  equal  to  the  osmotic  pressure  of  the  metallic 

1  Ztschr.  phys.  Chem.,  4,  151. 


APPLICATIONS   OF  THE  THEORY  235 

ions  in  the  solution.  An  electromotive  force  exists  here, 
also,  between  the  metal  and  the  solution,  but  in  the  reverse 
direction  from  the  case  first  considered. 

The  third  case  is  where  the  solution-tension  of  the 
metal  is  just  equal  to  the  osmotic  pressure  of  the  metallic 
ions  in  the  solution.  Just  as  soon  as  the  metal  touches 
the  solution,  equilibrium  is  established.  Ions  neither  dis- 
solve from  the  metal,  nor  separate  from  the  solution. 
There  is  no  double  electrical  layer  formed,  and  there 
is  no  difference  in  potential  between  the  metal  and  the 
solution. 

If  now  we  inquire  which  metals  have  high,  and  which 
low  solution-tensions,  we  will  find  that  magnesium,  zinc, 
aluminium,  cadmium,  iron,  cobalt,  nickel,  and  the  like, 
are  always  negative  when  immersed  in  solutions  of  their 
own  salts.  This  means  that  the  solution-tension  of  the 
metal  is  always  greater  than  the  osmotic  pressure  of 
the  metal  ion,  in  any  solution  of  their  salts  which  can  be 
prepared.  If,  on  the  other  hand,  we  take  gold,  silver, 
mercury,  copper,  etc.,  we  usually  find  the  metal  positive 
when  immersed  in  a  solution  of  its  salt.  This  means  that 
the  solution-tension  of  the  metal  is  so  small,  that  it  is  less 
than  the  osmotic  pressure  of  the  metallic  ion  in  the  solu- 
tion. When  a  very  dilute  solution  of  salts  of  these  metals 
is  prepared,  the  osmotic  pressure  of  the  metallic  ion  may 
become  less  than  the  very  slight  solution-tension  of  these 
metals  ;  and  then  the  metal  would  be  negative  with  respect 
to  its  solution. 

We  have,  thus  far,  spoken  chiefly  of  the  solution-tension 
of  metals,  which  tends  to  drive  the  metal  over  into  cations. 
Substances  which  can  pass  over  into  anions  have  also  a 


236  ELECTROLYTIC  DISSOCIATION 

solution-tension,  as  is  pointed  out  by  Le  Blanc.1  If  the 
chlorine  ions  in  a  solution  had  an  osmotic  pressure  which 
was  greater  than  the  solution-tension  of  chlorine,  the  chlo- 
rine ions  would  pass  over  into  ordinary  chlorine.  But 
Le  Blanc  adds,  that,  as  far  as  we  know,  all  substances 
which  can  yield  negative  ions  have  a  high  solution-tension. 

Constancy  of  Solution-tension.  —  It  was  supposed  for  a 
time,  that  the  solution-tension  of  a  metal  is  a  characteristic 
constant  for  the  substance.  This  view  was  held  by  Ostwald 
and  developed  in  his  Lehrbuch.  On  page  852  it  is  stated 
that  "the  value  P,  of  the  electrolytic  solution-pressure,  is 
a  constant  peculiar  to  the  metal,  which  depends  upon  the 
temperature  only,  and  generally  increases  with  increasing 
temperature." 

So  far  as  we  know,  this  holds  for  a  given  solvent,  but 
does  not  apply  to  different  solvents.2  Jones  has  found 
that  the  solution-tension  of  metallic  silver,  when  immersed 
in  an  alcoholic  solution  of  silver  nitrate,  is  only  about  one- 
twentieth  of  that  in  an  aqueous  solution.  We  can,  there- 
fore, regard  solution-tension  as  a  constant  only  for  any 
given  solvent  in  which  the  salts  of  the  metal  are  dissolved. 
Indeed,  this  is  what  we  would  expect,  when  we  consider 
that  nearly  every  substance  dissolves  differently  in,  or  has 
a  specific  solution-tension  towards,  every  solvent.  If  the 
substances  which  dissolve  readily  in  solvents,  vary  so 
greatly  from  solvent  to  solvent,  as  we  know  they  do,  why 
should  not  substances  which  are  only  slightly  soluble,  such 
as  the  metals,  show  this  same  difference  ? 

Calculation  of  the  Difference  in  Potential  between  Metal 

1  Lehrb.  der  Elektrochemie,  p.  121. 

2  Ztschr.  phys.  Chem.,  14,  346 ;  Phys.  Rev.,  2,  8l. 


APPLICATIONS   OF  THE  THEORY  237 

and  Solution.  —  The  difference  in  potential  between  a 
metal  of  solution-tension  Pt  and  a  solution  of  one  of  its 
salts  in  which  the  metal  ion  has  an  osmotic  pressure/,  can 
be  calculated  as  follows. 

When  a  substance  of  solution-tension  P  is  converted 
into  ions  of  osmotic  pressure  P,  no  work  is  done.  There- 
fore, to  convert  a  substance  of  solution-tension  P  into  ions 
of  osmotic  pressure  /,  the  maximum  work  to  be  obtained 
is  the  same  as  that  obtained  by  transferring  the  ions  from 
osmotic  pressure  P  to  osmotic  pressure  /.  Now  we  have 
seen  that  the  gas  laws  apply  to  the  osmotic  pressure  of 
solutions,  and  the  amount  of  work  can  be  calculated  from 
a  gas  in  passing  from  gas  pressure  P  to  gas  pressure  /. 
If  we  deal  with  a  gram-molecular  weight,  we  have  seen 
(p.  228)  this  to  be:  — 

RT\*~ 

P 

We  have  seen  that  this  osmotic  work  is  equal  to  the 
electrical  work  for  an  isothermal  transformation.  The 
electrical  work  is  the  potential  times  the  amount  of  elec- 
tricity. If  we  are  dealing  with  gram-molecular  quantities, 
it  is  irveQ. 

Equating  these  two  values,  we  have :  — 

p 

R  T  In  —  > 


or,  if  the  ions  are  univalent,  v  =  i,  when  we  have: 


'o 


238  ELECTROLYTIC   DISSOCIATION 

r>  >-p 

Now  we  know,  from  page  230,  that  =  0.0251    volt 

eo 
Passing  from  natural  to  Briggsian  logarithms,  this  becomes 

0.058  volt. 

The  potential  between  metal  and  solution  is,  then,  when 
7- =290°:- 

7T  =  0.058  log 

P 

We  have  learned,  thus  far,  how  to  calculate  the  electro- 
motive force  of  elements  from  the  osmotic  pressures  of 
the  solutions  around  the  electrodes ;  and  also  how  to  Cal- 
culate the  potential  between  a  metal  and  the  solution  of 
one  of  its  salts  in  which  the  metal  is  immersed.  With 
these  two  conceptions  in  mind,  we  will  now  study  a  few 
elements  to  see  how  these  principles  are  applied. 

Types  of  Cells.  —  If  the  chemical  process  in  the  cell 
remains  the  same  during  the  time  it  is  closed,  the  cell 
is  constant.  If  the  chemical  process  changes,  it  is 
inconstant. 

Constant  elements  differ  among  themselves.  Through 
some  of  these  we  can  send  a  current  in  the  opposite  direc- 
tion without  changing  their  electromotive  force.  This  class 
of  constant  elements  is  termed  reversible.  This  applies  to 
elements  in  which  the  electrodes  are  immersed  in  solutions 
of  their  salts.  Take  as  an  example  the  Daniell  element. 
This  consists  of  a  bar  of  zinc  immersed  in  a  solution  of 
zinc  sulphate,  and  a  bar  of  copper  in  a  solution  of  copper 
sulphate.  When  the  current  is  passed  in  the  opposite 
direction  through  this  cell,  its  nature  is  not  changed. 
The  normal  action  is  that  the  zinc  dissolves  and  copper 
separates.  When  a  current  is  passed  in  the  opposite 


APPLICATIONS   OF  THE  THEORY  239 

direction,  copper  dissolves  and  zinc  separates.  But  neither 
process  changes  the  nature  of  the  cell. 

Concentration  Elements  of  the  First  Type.  —  We  will 
first  consider  a  very  simple  type  of  a  reversible  element, 
the  two  electrodes  being  of  the  same  metal,  and  are 
immersed  in  solutions  of  the  same  salt  of  that  metal,  the 
solutions  having  different  concentrations.  To  take  a  con- 
crete example  :  Two  bars  of  metallic  zinc  are  immersed  in 
solutions  of  zinc  chloride,  the  one  bar  in  a  tenth-normal 
solution  of  the  salt,  the  other  in  a  hundredth-normal  solu- 
tion. The  two  solutions  are  connected  by  a  tube  filled 
with  either  solution.  When  the  two  zinc  bars,  which  are 
the  electrodes,  are  connected  externally,  the  current  flows, 
and  we  have  an  element.  Ostwald  defines  a  cell  or  element 
as  any  device  in  which  chemical  energy  is  converted  into 
electrical. 

The  only  difference  between  the  two  sides  of  this  element 
is  in  the  concentration  of  the  electrolytic  solutions.  The 
element  is,  therefore,  termed  a  "concentration  element." 
Further,  since  the  salt  of  the  metal  is  soluble,  this  is  termed 
a  "concentration  element  of  the  first  class,"  to  distinguish 
it  from  other  concentration  elements  which  will  be  taken 
up  later. 

Take  the  example  given  above,  of  two  bars  of  zinc  in 
two  solutions  of  zinc  chloride  of  different  concentrations. 
The  action  of  the  cell  is  such  as  to  make  the  two  solutions 
become  more  and  more  nearly  of  the  same  concentration. 
The  more  dilute  solution  becomes  more  concentrated,  and 
the  more  concentrated  more  dilute,  until  when  the  two 
become  equal  the  element  ceases  to  act.  Zinc  then  passes 
into  solution  in  the  more  dilute  solution,  and  zinc  ions 


240  ELECTROLYTIC  DISSOCIATION 

separate  as  metal  on  the  bar  from,  the  more  concentrated 
solution.  The  electrode  in  the  more  concentrated  solution 
is  always  positive,  since  metallic  ions  are  giving  up  their 
positive  charges  to  it,  and  separating  as  metal  upon  it. 
The  electrode  in  the  more  dilute  solution  is  negative, 
because  ions  are  passing  from  it  into  the  solution,  and 
carrying  with  them  positive  charges,  which  come  from 
the  electrode.  In  an  element  of  this  kind,  the  current 
always  flows  on  the  outside,  from  the  electrode  which  is 
immersed  in  the  more  concentrated  solution. 

The  action  of  this  cell  is  just  what  we  would  expect 
The  solution-tension  of  the  zinc  is  the  same  on  both  sides 
of  the  cell.  The  osmotic  pressure  of  the  zinc  ions  is,  of 
course,  greater  in  the  more  concentrated  solution.  The 
osmotic  pressure,  which  works  directly  against  the  solu- 
tion-tension, will  cause  the  ions  to  separate  from  the 
solution  in  which  this  pressure  is  the  greater.  The 
electromotive  force  of  such  an  element  would  be  the 
difference  in  the  potential  upon  the  two  sides  of  the  cell. 

RT  .     P     RT  .     P     RT  .     fa 

TT  = In -In—  =  -    -  In  ^- 

veQ        pi      ve^        /!       veQ         /2 

Here  *u  is  the  valence  of  the  cation,  /x  and  />2  the 
osmotic  pressures  of  the  zinc  ions  in  the  two  solutions. 
This,  however,  does  not  take  into  account  the  changes  in 
the  concentrations  of  the  solutions,  which  are  taking  place 
while  the  current  is  passing. 

If  e0  electricity  passes  from  the  electrode  into  the 
electrolyte,  a  gram-molecular  weight  of  univalent  cations 
separates  from  the  electrode,  dissolves,  and  increases  by 
unity  the  concentration  around  this  electrode.  But,  at 


APPLICATIONS   OF  THE  THEORY  241 

the  same  time,  cations  are  moving  from  this  electrode, 
with  the  current,  over  towards  the  other  electrode.  The 
amount  depends  upon  the  relative  velocities  of  anion  and 
cation.  If  we  represent  the  relative  velocity  of  cation  by 
c,  and  of  anion  by  a,  the  number  of  the  cations  which  will 

move  over  with  the  current  is  -  •     The  increase  in  the 

c  +  a 

concentration,  due  to  a  gram-molecular  weight  of  cations 
passing  into  solution,  is  then  :  — 

c  a 

y          _    _    —   _  m 

c  +  a~~  c  +  a 

This  factor  is  to  be  multiplied  into  the  former  equation 
to  obtain  the  osmotic  work,  which  can  then  be  equated  to 
its  equal,  the  electrical  energy.  Let  n{  represent  the  number 
of  ions  in  the  electrolyte.  Taking  into  account  both  sides 
of  the  cell,  we  have  :  - 


c  +  a      ve0          /2 

or,  ,r  =  —  -'  0.0002  riog^l- 

c  -H  a   v  /2 

According  to  this  formula,  the  only  variables  are  p^ 
and  /2,  the  osmotic  pressures  of  the  cation  in  the  two 
solutions  around  the  electrodes.  The  electromotive  force 
of  such  elements  should  depend  only  upon  the  relative 
osmotic  pressures  of  the  solutions,  and  not  upon  the 
absolute  osmotic  pressures.  This  has  been  found  to  be 
true.  The  electromotive  force  should  also  be  independent 
of  the  kind  of  zinc  salt  used,  provided  the  salt  is  soluble, 
and  yields  the  same  number  of  zinc  ions  in  each  solu- 
tion as  the  salt  in  question.  Thus  the  chloride  could  be 
replaced  by  the  bromide,  iodide,  nitrate,  etc.,  of  such 


242  ELECTROLYTIC  DISSOCIATION 

concentration  that  the  osmotic  pressure  of  the  zinc  ions 
remained  the  same,  and  the  electromotive  force  of  the 
element  should  remain  unchanged,  and  such  again  is  the 
fact.  The  reason  for  this  will  be  seen  at  once  by  examin- 
ing the  last  equation;  since  it  is  only  the  osmotic  pressure 
of  the  cations  which  comes  into  play  —  the  anion  having 
nothing  whatever  to  do  with  the  electromotive  force  of 
the  element. 

The  electromotive  force  of  a  number  of  elements  of 
the  type  we  are  considering  has  been  measured,  and  to 
within  the  limits  which  could  reasonably  be  expected  has 
been  found  to  agree  with  that  calculated  from  the  above 
equation.  To  calculate  the  electromotive  force,  a  number 
of  quantities  must  be  measured,  c  and  a,  the  relative 
velocities  of  cation  and  anion,  must  be  determined ;  simi- 
larly, /!  and  /2,  the  osmotic  pressures  of  the  cations  in 
the  solutions,  must  be  ascertained  by  indirect  methods, 
which  involve  the  measurement  of  the  dissociation  of  these 
solutions.  Since  each  of  these  processes  introduces  an 
error  of  greater  or  less  magnitude,  we  could  not  expect  a 
very  close  agreement  between  the  electromotive  force  as 
measured  and  as  calculated.  When  we  take  all  of  these 
facts  into  account  the  agreement  is  often  surprisingly 
close. 

The  following  results,  obtained  by  Moser,  for  solutions 
of  copper  sulphate,  with  copper  electrodes,  are  cited  by 
Ostwald.1  The  concentrations  of  solutions,  I  and  II,  are 
the  number  of  parts  of  water  to  one  part  of  copper 
sulphate.  TT  is  the  electromotive  force  expressed  in 
thousandths  of  a  Daniell  cell.  The  unit  is  o.oon  volt. 

i  Lehrb.  d.  allg.  Chem.,  II,  p.  833. 


APPLICATIONS   OF  THE  THEORY  243 


I 

II 

it  OBSERVED    n  ( 

I^ALCUL/ 

128.5 

4.208 

27 

27.4 

6.352 

25 

23.8 

8.496 

21 

21.4 

17.07 

16 

15.8 

34.22 

IO 

10.3 

The  concentration  of  one  solution  was  maintained  con- 
stant throughout,  and  that  of  the  other  varied  at  will. 
The  agreement  in  these  cases  is  very  satisfactory. 

Concentration  Elements  of  the  Second  Type.  —  The  char- 
acteristic of  the  element  which  we  have  just  been  consid- 
ering is  that  the  metal  is  surrounded  by  one  of  its  soluble 
salts.  We  may  also  have  concentration  elements  in  which 
the  metal  is  surrounded  by  one  of  its  insoluble  salts ; 
thus,  silver  surrounded  by  silver  chloride.  In  the  latter 
case  we  must  have  present,  in  addition,  a  soluble  chloride ; 
and  the  soluble  chloride  must  be  of  different  concentra- 
tions on  the  two  sides  of  the  cell.  The  element  would 
consist  then  of  a  bar  of  silver,  surrounded  by  solid  silver 
chloride,  and  over  this  a  solution  of  some  chloride,  say 
potassium  chloride ;  and  on  the  other  side,  a  bar  of  silver 
surrounded  by  solid  silver  chloride,  and  over  this  a  solu- 
tion of  potassium  chloride,  of  different  concentration  from 
that  used  on  the  side  first  described. 

This  element  is  termed  a  concentration  element  of  the 
second  class. 

The  action  of  this  cell  will  be  such  as  to  dilute  the 
more  concentrated  solution  of  potassium  chloride,  and  to 
concentrate  the  more  dilute  solution.  Silver  dissolves 
from  the  electrode  surrounded  by  the  more  concentrated 
potassium  chloride,  and  the  ions  of  silver  unite  with  the 


244  ELECTROLYTIC   DISSOCIATION 

chlorine  ions,  and  solid  silver  chloride  is  formed.  The 
potassium  ions  move  with  the  current  over  to  the  other 
side  of  the  element,  and  form  potassium  chloride  with  some 
of  the  chlorine  which  was  there  in  combination  with  silver 
as  silver  chloride.  This  silver  then  separates  as  metal 
upon  the  electrode.  In  this  way  the  more  concentrated 
potassium  chloride  becomes  more  dilute,  and  the  more 
dilute  becomes  more  concentrated. 

The  electrode  immersed  in  the  more  concentrated  po- 
tassium chloride  is  the  one  from  which  silver  ions  separate ; 
therefore,  this  is  the  negative  pole.  The  pole  in  the 
more  dilute  solution  of  potassium  chloride,  receiving  silver 
ions,  is  positive.  The  current  then  flows  upon  the  outside, 
from  the  pole  in  the  more  dilute  potassium  chloride,  to 
the  pole  in  the  more  concentrated. 

This  is  exactly  the  reverse  of  what  takes  place  in  a 
concentration  element  of  the  first  type.  There,  as  we 
have  seen,  the  current  flows  on  the  outside,  from  the 
pole  surrounded  by  the  more  concentrated  electrolyte. 

The  electromotive  force  of  a  concentration  element  of  the 
second  type  is  calculated  in  a  manner  perfectly  analogous 
to  that  employed  with  concentration  elements  of  the  first 
type.  The  electromotive  force  TT  is  equal  to  the  dif- 
ference in  the  potential  at  the  two  poles :  — 

RT  .     P     RT  .     P     RT  .     pl 
TT  = In In  —  =-   *  In  "• 

veQ        pi       ve<>        pl       veQ         p^ 

As  in  the  case  of  the  concentration  element  of  the  first 
class,  this  does  not  take  into  account  the  changes  in  the 
concentrations  of  the  electrolytes  which  are  taking  place. 
At  the  anode  the  metallic  silver  is  passing  into  solution, 


APPLICATIONS  OF  THE  THEORY  245 

and  when  eQ  electricity  is  allowed  to  flow,  a  gram- 
molecular  weight  of  the  silver  will  pass  over  into  ions  — 
will  dissolve.  This  will  change  the  concentration  of  the 
potassium  chloride  around  this  pole  by  —  i.  But  at  the 
same  time  potassium  is  moving  with  the  current,  and 
chlorine  in  the  opposite  direction,  and  this  further  changes 

the  concentration.     If  we  represent  the  relative  migration 

+ 
velocities  of  K  and  Cl,  respectively,  by  c  and  a,  the  total 

change  in  concentration  around  the  anode  will  be :  — 

-i   i      a  c 

c  +  a         c+a 

The  change  in  concentration  around  the  cathode  would 
be,  of  course :  — 


This  factor :  — 


must  be  multiplied  into  the  above  expression  for  electro- 
motive force ;  when  taking  into  account  both  sides  of  the 
cell,  we  have :  — 


7T 


c  +  a     ve0          /2 

2  C      Hi  T-  i        P\ 

-  0.0002  Tlog^i; 


where  n{  is,  as  before,  the  number  of  ions  yielded  by 
the  electrolyte,  and  v  the  valence  of  the  cation.  The 
electromotive  force  of  a  number  of  such  elements  has 
been  measured  by  Nernst.1  Mercury  was  used  as  the 
metal,  since  it  could  easily  be  obtained  in  pure  condition. 

1  Ztschr.  phys.  Chem.,  4,  159. 


246 


ELECTROLYTIC   DISSOCIATION 


It  was  covered  with  an  insoluble  salt  of  mercury,  and  the 
soluble  electrolyte  then  added.  The  chloride,  bromide, 
acetate,  and  hydroxide  of  mercury  were  used,  and  the 
soluble  electrolyte  on  both  sides  of  the  cell  must  con- 
tain the  same  anion  as  the  salt  of  mercury  which  was 
employed.  If  the  chloride  was  used,  the  soluble  elec- 
trolyte must  be  a  chloride.  If  the  hydroxide  of  mercury 
was  employed,  a  soluble  hydroxide  must  be  used,  and  so 
on. 

Some  of  the  combinations  which  were  made  and  meas- 
ured by  Nernst  are  given  in  the  following  table.  The  first 
column  contains  the  soluble  electrolyte  which  was  em- 
ployed. Columns  II  and  III  give  the  concentrations  of 
the  solutions  of  this  electrolyte  on  the  two  sides  of  the  cell. 
"  TT  calculated  "  is  the  electromotive  force  calculated  from 
the  preceding  formula,  and  "  IT  found  "  is  the  electromotive 
force  of  the  combination,  as  measured  by  Nernst. 


I 

SOLUBLE 

ii 

III 

It 

7T 

ELECTROLYTE 

CONCENTRATION  i 

CONCENTRATION  2 

CALCULATED 

FOUND 

HC1 

0.105 

O.OlS 

0.0717 

0.0710 

HC1 

O.I 

0.01 

0.0939 

0.0926 

HBr 

O.I26 

0.0132 

0.0917 

0.0932 

KC1 

O.I25 

0.0125 

0.0542 

0.0532 

NaCl 

O.I25 

0.0125 

0.0408 

0.0402 

LiCl 

O.I 

0.01 

0.0336 

0-0354 

NH4C1 

O.I 

0.01 

0.0531 

0.0546 

NaBr 

0.125 

0.0125 

0.0404 

0.041  7 

CH3COONa 

0.125 

0.0125 

0.0604 

0.0660 

NaOH 

0-235 

0.030 

0.0183 

0.0178 

KOH 

O.I 

O.OI 

0.0298 

0.0348 

NH4OH 

0-305 

0.032 

0.0188 

0.024 

APPLICATIONS   OF  THE  THEORY  247 

Liquid  Elements.  —  It  has  long  been  known  that  there 
may  be  differences  in  potential  at  the  contact  of  two  solu- 
tions of  electrolytes.  This  can  be  shown  by  constructing 
an  element  in  which  the  two  electrodes  are  of  the  same 
metal,  and  immersed  in  the  same  solution  of  the  same 
electrolyte.  There  can,  therefore,  be  no  difference  in  po- 
tential between  the  two  metals,  nor  between  the  metals 
and  electrolytes,  for  the  tensions  between  the  metals  and 
electrolytes  are  the  same  on  the  two  sides,  and  act  in  direct 
opposition  to  one  another.  If  two  solutions  of  electrolytes 
of  different  concentrations  are  introduced  into  the  circuit 
between  the  solutions  in  which  the  electrodes  are  im- 
mersed, we  will  have  an  element  with  a  certain  definite 
electromotive  force.  A  typical  liquid  element  would  be 
the  following :  — 

Mercury-mercurous  chloride. 

—  potassium  chloride. 
10 

-^-potassium  chloride. 
100 

-^—  hydrochloric  acid. 
100   ' 

—  hydrochloric  acid. 
10 

—  potassium  chloride. 
10 

Mercurous  chloride-mercury. 

Theory  of  the  Liquid  Element.  —  The  first  satisfactory 
theory  of  the  liquid  element  we  owe  to  Nernst.1  What  is  the 

1  Ztschr.  phys.  Chem.,  4,  140. 


248  ELECTROLYTIC  DISSOCIATION 

source  of  the  differences  in  potential  in  liquid  elements  ? 
That  differences  in  potential  should  exist  in  electrolytes 
there  must  be  a  lack  of  uniform  distribution  of  ions.  The 
region  which  is  positive  must  contain  an  excess  of  cations, 
and  that  which  is  negative,  an  excess  of  anions.  The  cause 
of  this  lack  of  uniform  distribution  of  ions  is  to  be  found 
in  the  different  velocities  with  which  the  different  ions 
diffuse. 

Take  the  case  of  a  solution  of  hydrochloric  acid  in  con- 
tact with  pure  water.  The  hydrogen  and  chlorine  ions 
in  the  solution  of  the  acid  are  present  in  the  same  number. 
They  are,  therefore,  under  the  same  osmotic  pressure,  and 
are  driven  with  the  same  force  into  the  water.  But  they 
move  with  very  different  velocities,  from  regions  of  higher 
to  those  of  lower  osmotic  pressure.  Hydrogen  is,  as  we 
have  seen,  the  swiftest  of  all  ions,  and  moves  very  much 
faster  than  chlorine.  It  will  thus  diffuse  into  the  water 
more  rapidly  than  chlorine,  and  will  tend  to  separate  from 
the  chlorine.  But  the  positive  ions  cannot  separate  from 
the  negative  ions,  without  producing  a  separation  of  the 
two  kinds  of  electricity.  There  will  result,  therefore,  elec- 
trostatic attractions  between  the  layers,  which  will  retard 
the  hydrogen  ions  and  accelerate  the  chlorine  ions,  until 
the  two  have  the  same  velocity. 

Differences  in  potential  will  result;  and  always  in  the 
sense,  that  the  water  or  the  more  dilute  solution  will  have 
the  sign  of  the  swifter  ion.  Hydrogen  being  the  swiftest 
of  all  ions,  water,  or  the  more  dilute  solution  of  acid,  is 
always  positive  with  respect  to  the  more  concentrated. 
Next  to  hydrogen,  in  order  of  velocity,  comes  hydroxyl. 
Water,  or  the  more  dilute  solution  of  a  base,  must,  there- 


APPLICATIONS   OF  THE  THEORY  249 

fore,  always  be  negative  with  respect  to  the  more  con- 
centrated. 

Nernst  has  shown  not  only  how  it  is  possible  to  account, 
qualitatively,  for  the  differences  in  potential  between  elec- 
trolytes, but  has  furnished  us  also  with  a  method  of  calcu- 
lating these  differences  quantitatively. 

Given  two  solutions  of  different  concentrations  of  an 
electrolyte  like  hydrochloric  acid,  which  is  composed  of  a 
univalent  cation  and  a  univalent  anion.  Let  the  velocity 
of  the  cation  be  c,  and  that  of  the  anion  a.  Let  p^  be  the 
osmotic  pressure  of  both  ions  in  the  more  concentrated 
solution,  and  /2  the  osmotic  pressure  in  the  more  dilute. 
If  eQ  electricity  is  passed  from  the  more  concentrated  to 
the  more  dilute  solution,  — - —  of  a  gram-equivalent  of 

cations  will  move  with  the  current,  and  — - —  of  a  gram- 

c  +  a 

equivalent  of  anions  will  move  against  the  current. 

of  cations  have  moved  from  a  region  of  greater  to 


c  +  a 
one  of  less  osmotic  pressure.     The  work  is :  — 


c  +  a 

But  of  anions  have  moved  from  a  region  of  lower 

c  +  a 

into  one  of  higher  osmotic  pressure.     The  work  done  upon 
them  is :  — 


c  +  a  /2 

The  total  gain  is  the  difference  between  these  two :  — 

l^ 
c  +  a 


250  ELECTROLYTIC   DISSOCIATION 

Equating    this    against   the   electrical   energy  7ir0,  we 

have:—  c_a  RT       p 

TT  =  -         -  In  ±f  ; 

c  +  a     eo         Pi 

or,  TT  =  -  -  0.0002  T  log  —  . 

c  +  a  &  /2 

If  c  is  greater  than  a,  the  more  dilute  solution  is  positive, 
as  already  stated,  and  the  current  flows  on  the  outside, 
from  the  more  dilute  solution  to  the  more  concentrated. 
If  a  is  greater  than  c,  the  more  dilute  solution  is  negative, 
and  the  current  flows  in  the  opposite  direction. 

If  the  velocities  of  the  two  ions  are  equal  (c  =  a),  the 
right  member  of  the  above  equation  becomes  zero,  and  there 
is  no  electromotive  force.  It  is,  therefore,  impossible  to 
construct  a  liquid  element  from  solutions  of  an  electrolyte 
whose  cation  and  anion  have  the  same  velocities.  If  the 
valence  of  either  ion  is  greater  than  unity,  this  must  be 
taken  into  account.  If  we  represent  the  valence  of  the 
cation  by  v,  and  that  of  the  anion  by  vlt  the  above  ex- 
pression becomes  :  — 


0.0002 


T  log  £. 
& 


c  +  a 

Nernst  prepared  liquid  elements  and  determined  their 
electromotive  force.  He  then  calculated  the  electromotive 
force  from  the  above  equation,  and  compared  the  values 
found  experimentally  with  those  from  calculation. 

The  following  element  already  referred  to  was  con- 
structed:-  1234 

Hg-HgCl-KCl-KCl-HCl-HCl-KCl-HgCl-Hg. 
n          n  n          n          n 

IO         100          100         10  IO 


APPLICATIONS  OF  THE  THEORY  251 

The  potential  differences  at  the  ends  are  equal  and 
opposite,  and  therefore  equalize  one  another.  The  four 
differences  in  potential  which  must  be  taken  into  account 
are  indicated  above.  But  the  potential  differences  are 
dependent  upon  the  relative  not  upon  the  absolute  osmotic 
pressures.  The  potentials  at  2  and  4  are,  therefore,  equal 
and  opposite,  and  can  also  be  left  out  of  account.  This 
leaves  the  potentials  at  I  and  3,  and  these  can  be  calcu- 
lated by  the  method  already  given.  Let  cl  and  a1  be  the 
relative  velocities  of  potassium  and  chlorine  ions,  and  c2 
and  a2  the  relative  velocities  of  hydrogen  and  chlorine 
ions;  the  electromotive  force  of  this  element  would  be 
calculated  as  follows,  from  the  equation  just  deduced. 
The  electromotive  force  would  be  the  difference  between 
these  two  potentials  :  — 


p  and  /j  are  the  osmotic  pressures  of  the  potassium  and 
chlorine  ions  in  the  more  concentrated  and  more  dilute 
solutions,  respectively;  pl  and//  the  osmotic  pressures  of 
the  hydrogen  and  chlorine  ions  in  the  solutions  of  hydro 

chloric  acid. 

/=/ 

/i     Pi 
Introducing  this  into  the  last  equation,  we  have  :  — 


Q  ! 

or,  TT  =  -  Tl      L. 

* 


252  ELECTROLYTIC   DISSOCIATION 

This  is  the  expression  for  calculating  the  electromotive 
force  in  liquid  elements,  like  the  above,  where  the  valence 
of  the  cation  is  the  same  as  that  of  the  anion.  If  they  are 
different,  we  will  represent  the  valence  of  the  cations  by 
v  and  vr,  and  that  of  the  anions  by  ^  and  v-^ ;  the  equa- 
tion for  the  electromotive  force  would  then  become  :  — 


TT  = 


0.0002  Tlog  —  • 
P\ 


The  electromotive  force  of  the  liquid  elements  which 
have  been  studied,  as  calculated  from  the  above  equation, 
agrees  with  that  measured,  to  within  the  limits  of  experi- 
mental error. 

It  should  be  observed,  that  the  expression  deduced 
above  holds  only  for  the  potential  at  the  contact  of  solu- 
tions of  the  same  electrolyte,  the  solutions  being  of  dif- 
ferent concentrations.  If  different  electrolytes  are  used, 
we  have  no  general  means  of  calculating  the  potential  at 
their  surface  of  contact. 

It  should  be  stated  before  leaving  the  subject  of  liquid 
elements,  that  the  potential  at  the  contact  of  two  solutions 
is  usually  not  great,  and  that  the  electromotive  force  of 
liquid  elements  is  in  general  not  large. 

Sources  of  Potential  in  a  Concentration  Element.  —  We 
may  now  analyze,  more  closely,  the  electromotive  force  in 
a  concentration  element,  in  the  light  of  what  we  have 
learned  about  the  liquid  element.  Thus  far,  we  have  dealt 
with  the  concentration  element  as  if  the  only  sources  of 
the  potential  were  at  the  points  of  contact  of  the  electrodes 
and  the  solutions.  And  indeed  this  is  practically  true  in 


APPLICATIONS   OF  THE  THEORY  253 

the  cases  of  the  concentration  element  which  we  have 
studied. 

We  have  learned  from  the  study  of  the  liquid  ele- 
ment, that  the  plane  of  contact  of  two  solutions  of  an 
electrolyte  is  also  a  seat  of  potential.  In  the  concentra- 
tion element  there  is  always  such  a  contact  between  two 
solutions  of  the  electrolyte,  and  this  must  be  a  source  of 
potential.  In  the  concentration  element  which  we  have 
studied,  this  potential  is  so  small  that  it  can  practically  be 
neglected.  While  the  potential  between  solutions  is  usually 
small,  it  may,  however,  easily  assume  proportions  which 
must  be  taken  into  account.  We  must  now  see  how  it  is 
possible  to  calculate  the  potential  at  the  contact  of  the 
two  solutions  in  the  concentration  element.  We  can  then 
analyze  the  electromotive  force  of  a  concentration  element 
into  its  three  constituents,  and  calculate  the  magnitude  of 
the  potential  at  each  electrode,  and  also  at  the  surface  of 
contact  of  the  electrolytes. 

Let  the  potential  at  one  electrode  be  TT',  at  the  other 
electrode  IT",  and  at  the  contact  of  the  two  electrolytes 
7rlrf.  The  values  of  these  potentials  are  calculated  by 
means  of  the  following  formulas  :  — 

p 
7rf  =  0.0002  rio   —  ; 


P 
—  0.0002  Tlog  — 


IT'"  =  0.0002  T-        log 

c  +  a     & 


These    equations    obtain    for    univalent   ions.      If   the 
valence  of  the  ion  is  greater  than  one,  this  must  be  taken 


254  ELECTROLYTIC   DISSOCIATION 

into  account  in  the  way  already  described.  The  sum  of 
the  three  potentials  must  then  be  the  potential  of  the  con- 
centration element. 

IT'  +  TT"  =  -  0.0002  Tlog  &  ; 

Pi 

(rf  +  „.")  +  TT'"  =  0.0002  r  -^-  log  &• 

c  +  a        pi 

This  must  be  the  same  as  the  equation  already  deduced 
(p.  241)  for  the  concentration  element.  It  will  be  seen  to 
be  the  case,  if  we  consider  that  «,-  =  2,  and  v  for  univalent 
ions  equals  I. 

We  can  thus  calculate  the  magnitude  of  the  three 
sources  of  potential  in  a  concentration  element  of  the  first 
class.  An  element  of  this  class  has  been  chosen,  since 
the  relations  are  somewhat  simpler.  The  main  sources  of 
potential  are  at  the  contact  of  electrode  and  electrolyte, 
while  a  very  small  potential  exists  at  the  contact  of  the 
two  electrolytes.  In  elements  of  this  kind,  it  is  perfectly 
clear  that  there  is  no  potential  where  the  two  electrodes 
come  in  contact,  because  these  are  of  the  same  metal. 

The  Electromotive  Force  of  the  Daniell  Element.  —  The 
elements  which  we  have  considered  thus  far  have  both 
electrodes  of  the  same  metal.  The  solution-tension  of  the 
metal  was,  therefore,  the  same  upon  both  sides  of  the  cell, 
and  being  of  equal  value  and  opposite  sign,  it  disappeared 
from  the  equation  for  the  electromotive  force  of  the 
element. 

In  most  of  our  common  elements,  however,  two  metals 
are  used  as  electrodes,  or  a  metal  and  carbon.  It  is  evi- 
dent that  in  these  cases  the  solution-tension  of  the  electrode 


APPLICATIONS  OF  THE  THEORY  255 

must  be  taken  into  account,  since  it  is  different  for  different 
metals. 

The  Daniell  element  is  taken  as  a  type  of  the  two  metal 
elements  with  which  we  are  so  familiar.  The  application 
of  our  fundamental  equation  to  this  element  will  serve  as 
an  example  of  the  way  in  which  it  may  be  applied  to 
other  well-known  elements. 

The  Daniell  element  consists  of  zinc  in  zinc  sulphate, 
and  copper  in  copper  sulphate.  Zinc  dissolves  and  copper 
separates  from  the  solution.  The  zinc  electrode  is  there- 
fore negative,  and  the  copper  positive,  the  current  passing 
on  the  outside  from  the  copper  to  the  zinc.  The  electro- 
motive force  is  equal  to  the  difference  in  potential  at  the 
two  electrodes,  since  the  potential  at  the  contact  of  the 
zinc  sulphate  and  copper  sulphate  is  so  slight  that  we  can 
practically  disregard  it. 

Representing   the   potential   at   the   two   electrodes  by 


and  7r2,  we  have  :  — 


RT  .    P 
-  In  —  ; 


RT  .     P1 
-  In  —  - 


in  which  P  and  Pl  are  the  solution-tensions  of  the  two 

metals. 

RT  .    P     RT  .    Pl 
TT-—  7r2  =  7r  =  —   -In  ---   -In  —  *• 

2e0        p       2eQ        pl 

In  the  light  of  this  example,  the  application  of  the  con- 
ceptions here  developed,  to  other  special  cases,  should  be 
a  simple  matter. 


256  ELECTROLYTIC  DISSOCIATION 

The  Gas-battery.  —  The  typical  gas-battery  consists  of 
an  electrolyte,  two  gases  which  can  act  chemically  upon 
one  another,  and  two  platinum  electrodes  which  are  partly 
surrounded  by  the  electrolyte,  and  partly  by  the  gases. 

Take  as  a  simple  example,  hydrogen  over  one  electrode 
and  chlorine  over  the  other,  the  electrolyte  hydrochloric 
acid,  and  the  electrodes  platinum.  Hydrogen  and  chlorine 
will  pass  into  solution  at  the  two  poles  until  there  is  an 
equilibrium  between  the  force  driving  these  substances 
into  solution  (solution-tension),  and  the  osmotic  pressure 
of  the  hydrochloric  acid  solution,  which  acts  against  the 
above-named  force.  The  hydrogen  pole  is  negative,  since 
the  solution-tension  of  the  hydrogen  is  greater  than  the 
osmotic  pressure  of  the  solution ;  the  hydrogen  atoms 
becoming  ions  by  taking  positive  electricity  from  the 
platinum  electrode,  which  thus  becomes  negative.  Exactly 
the  opposite  result  is  obtained  at  the  other  electrode, 
chlorine  atoms  becoming  ions  by  taking  negative  electric- 
ity from  the  electrode,  which  therefore  becomes  positive. 

Ostwald l  has  shown  that  the  theory  of  Nernst  can  be 
applied  also  to  the  electromotive  force  of  the  gas-battery. 
He  has  worked  out  even  a  simpler  case  than  the  one 
given  above.  We  will  take  up  first  the  simplest  possible 
case,  where  we  have  the  same  gas,  say  hydrogen,  over 
both  electrodes,  the  hydrogen  upon  the  two  sides  being 
at  different  pressures. 

The  action  of  such  an  arrangement  would  be,  as  Ost- 
wald shows,  to  equalize  the  pressure  of  the  gas  upon  the 
two  sides  of  the  cell.  Hydrogen  must  pass  into  solution 
as  ions  upon  the  side  where  it  is  under  the  greater 

l  Lehrb.  d.  allg.  Chem.,  II,  9.895. 


APPLICATIONS  OF  THE  THEORY  257 

pressure,  and  ions  of  hydrogen  must  separate  as  gas  upon 
the  other  side  of  the  cell.  Upon  the  side  where  hydrogen 
atoms  are  becoming  ions,  they  take  positive  electricity 
from  the  electrode,  which  becomes  negative,  and  the  other 
electrode  positive,  because  positive  hydrogen  ions  are 
giving  their  charges  up  to  it.  We  have  here  an  analogue 
of  the  concentration  element,  and  the  electromotive  force 
can  be  calculated  in  a  similar  manner. 

The  electromotive  force  of  this  element  also  is  the 
difference  in  the  potential  upon  the  two  sides :  — 

RT  .     P      RT.     P 
TT  =  -    -  In In  —  ; 

*"o       A       veo       Pi 

where  P  is  the  solution-tension  of  hydrogen,  and  pl  and  p^ 
the  pressures  of  the  hydrogen  gas  upon  the  two  sides. 
The  solution-tension,  being  the  same  upon  both  sides  of 
the  cell,  disappears,  as  in  the  concentration  element,  and 

then  we  have:  — 

0.0002  T .      A 
TT  =  -        —  log  £*• 

v  A 

Since  for  hydrogen,  v—2.,  we  have:  — 

TT  =  0.0290  log  — • 
P<L 

Ostwald  1  has  also  calculated  the  electromotive  force  for 
a  gas-battery  consisting  of  two  gases.  But  as  this  has 
been  worked  out  much  more  fully  by  Smale,2  we  will  turn 
to  his  work. 

Take  the  case  of  oxygen  at  one  pole  and  hydrogen  at 
the  other. 

1  Loc.  cit.  2  ztschr.  phys.  Chem.,  14,  577,  and  16,  562. 


258  ELECTROLYTIC  DISSOCIATION 

Let  Pl  be  the  solution-tension  of  hydrogen. 
Let  PI  be  the  solution-tension  of  oxygen. 
Let  T  be  the  absolute  temperature. 
The  potential  at  the  hydrogen  pole  is  :  — 

p 

TTj  =  O.OOO2  T  log  — 
Pl 

Since  the  solution-tension  of  oxygen  is  negative:  — 
7r2  =  0.0002 


-J  —  ?T2  =  TT  ==  0.0002  7"log  —  —  0.0002  riog  ^; 


p  p 

TT  =  0.0002  7*  log  —  -  +  0.0002  riog  —  - 

Pl  /2 

The  theoretical  consequences  of  this  equation  are  very 
interesting.  Pl  and  P2,  the  solution-tensions  of  the  gases, 
are  independent  of  the  nature  and  concentration  of  the 
electrolyte  used  on  the  two  sides  of  the  element;  and 
/!  and  pi  are  practically  constant  for  solutions  of  nearly 
the  same  dissociation. 

Smale1  has  tested  this  point,  using  seven  acids,  three 
bases,  and  seven  salts.  The  concentrations  for  the  same 
electrolyte  vary  in  most  cases  from  o.i  to  o.ooi  normal. 
He  found  that  the  electromotive  force  of  the  hydrogen- 
oxygen  battery  was  practically  constant,  independent  of 
both  the  nature  and  concentration  of  the  electrolytes  used 
beneath  the  gases. 

A  few  results'  taken  from  the  work  of  Smale  will  bring 
out  this  fact. 

1  Loc.  cit. 


APPLICATIONS  OF  THE  THEORY  259 

ELECTROLYTE  USED  CONCENTRATION  NORMAL  E.M.F. 

HC1  o.i  0.998 

HC1  o.oi  1.036 

HC1  o.oo  i  1.055 

KOH  o.i  1.098 

KOH  o.oi  1.095 

KOH  o.ooi  1.093 

K2SO4  o.i  1.074 

K2SO4  o.oi  1.069 

K2SO4  o.ooi  1.069 

The  results  thus  agree  satisfactorily  with  the  deduction 
from  theory. 

If,  instead  of  oxygen,  other  gases,  as  chlorine,  are  used, 
the  electromotive  force  depends  upon  the  concentration  of 
the  electrolyte,  which  also  agrees  with  theory,  as  is  shown 
by  Smale. 

But  the  theory  admits  of  still  further  experimental  test. 

If  ¥the  electrodes  are  of  two  different  metals,  say  plati- 
num and  palladium,  and  are  surrounded  by  the  same 
gas  which  does  not  attack  them,  and  are  immersed  in  the 
same  electrolytes,  the  electromotive  force  at  each  electrode 
is  in  terms  of  the  theory  formulated  thus :  — 

p 

TJ-J  =  0.0002  T  log—  ; 
Pi 

p 

•7T2  =  O.OOO2  T  log  — -. 

p* 

P1  and  P2  are  the  solution-tensions  of  the  gas  in  plati- 
num and  palladium,  respectively ;  p^  and  /2  the  osmotic 
pressures  at  the  electrodes ;  which  are  equal  in  this  case, 


260  ELECTROLYTIC  DISSOCIATION 

since  the  same  electrolyte  is  used  on  both  sides.     There- 
fore, we  have  :  — 

p 

7Tl  —  7T2  —  7T  =  O.OOO2  T  log  —  1  VOltS. 


The  metal  electrodes  then  play  only  this  r61e,  they  offer 
a  large  surface  to  the  gas,  which  facilitates  its  solution  in 
them.  The  electromotive  force  of  such  an  element  should, 
therefore,  be  independent  of  the  nature  of  the  electrode 
used,  since  solution-tension  is  a  constant  for  any  given 
metal,  according  to  the  theory.  It  should,  further,  be  inde- 
pendent of  the  size  of  the  electrode. 

Both  of  these  points  were  tested  experimentally  by 
Smale.  The  nature  of  the  electrode,  whether  platinum, 
palladium,  or  gold,  had  no  influence  on  the  electromotive 
force.  The  size  of  the  electrode,  beyond  a  certain  point, 
had  no  influence.  A  certain  amount  of  surface  is,  how- 
ever, necessary  in  order  that  the  electrode  should  reach  its 
full  tension. 

This  work  of  Smale  furnishes  then  another  beautiful 
experimental  confirmation  of  the  consequences  of  that 
theory,  which  has  enabled  us  to  calculate  the  electromotive 
force  of  concentration  elements,  liquid  elements,  etc. 

A  number  of  other  types  of  elements  might  be  taken 
up,  and  their  electromotive  force  calculated  from  the 
method  of  Nernst,  which,  as  we  have  already  seen,  is 
based  upon  van't  Hoff's  laws  of  osmotic  pressure,  and 
Arrhenius's  theory  of  electrolytic  dissociation.  This  is, 
however,  not  necessary,  since  the  application  to  special 
cases  is  simple,  if  the  fundamental  principles  are  once 
grasped. 


APPLICATIONS  OF  THE  THEORY  261 

Chemical  Action  at  a  Distance.  —  Before  concluding  this 
section,  we  will  describe  a  phenomenon  of  unusual  inter- 
est. On  account  of  its  close  relation  to  solution-tension, 
it  should  appear  in  this  connection. 

In  1891,  a  paper  was  published  by  Ostwald,1  under  the 
surprising  title  "  Chemische  Fernewirkung."  It  was  sur- 
prising, because  chemical  action,  as  ordinarily  understood, 
takes  place  only  between  substances  which  are  close  to  one 
another.  Ostwald  begins  his  paper  by  calling  attention 
to  the  fact  that  amalgamated  zinc  is  not  dissolved  by 
dilute  acids,  but  if  the  zinc  is  surrounded  by  a  platinum 
wire,  it  is  dissolved  by  the  acid.  It  is  not  even  necessary 
for  the  platinum  wire  to  surround  the  zinc,  for  if  the  wire 
touches  the  zinc  at  any  one  point,  solution  will  take  place. 

Ostwald  suggests  that  the  zinc  and  platinum  wire  be 
joined  at  one  place,  and  then  the  free  ends  of  both  im- 
mersed in  a  vessel  containing,  say,  potassium  sulphate. 
Let  a  screen  of  some  porous  material  be  placed  between 
these  free  ends  of  the  platinum  and  zinc,  so  that  the  salt 
solution  around  the  one  is  separated  from  that  around  the 
other.  He  then  asks  the  question :  To  which  metal  must 
sulphuric  acid  be  added,  in  order  that  the  zinc  may  be 
dissolved  by  the  acid  ? 

"  The  question  seems  at  first  sight  to  be  absurd ;  since, 
in  order  that  the  zinc  should  dissolve,  it  appears  to  be  self- 
evident  that  the  acid  should  be  added  to  the  zinc.  If  we 
carry  out  the  experiment  we  find  exactly  the  reverse  to  be 
true.  The  zinc  does  not  dissolve  rapidly,  if  acid  is  added 
to  the  solution  of  potassium  sulphate  around  the  zinc.  If, 
on  the  contrary,  the  acid  is  added  to  the  solution  around 

1  Ztschr.  phys.  Chem.,  9,  540. 


262  ELECTROLYTIC  DISSOCIATION 

the  platinum,  the  zinc  dissolves  with  a  copious  evolution  of 
hydrogen  gas.  The  hydrogen  appears  on  the  platinum,  as 
is  always  the  case  when  zinc  is  in  combination  with  plati- 
num. To  dissolve  the  zinc  under  the  conditions  described, 
the  solvents  must  not  be  allowed  to  act  on  the  metal  to  be 
dissolved,  but  on  the  platinum  which  is  in.  contact  with  the 
zinc." 

A  number  of  other  cases  are  cited. 

Zinc  in  sodium  chloride  behaves  in  the  same  manner, 
when  hydrochloric  acid  is  added  to  the  platinum.  Cad- 
mium also  behaves  like  zinc.  Tin,  surrounded  by  sodium 
chloride,  dissolves  when  hydrochloric  acid  is  added  to 
the  platinum.  Aluminium  behaves  like  tin.  Silver  con- 
nected with  platinum  dissolves  in  .sulphuric  acid  when  a 
few  drops  of  chromic  acid  are  added  to  the  platinum. 
Gold  dissolves  in  sodium  chloride,  if  chlorine  is  brought 
in  contact  with  the  platinum. 

Experiment  to  demonstrate  Chemical  Action  at  a  Distance. 
Fill  a  beaker  with  a  solution  of  potassium  sulphate.  Take 
a  piece  of  glass  tubing  about  10  cm.  long  and  2  cm.  wide, 
and  close  the  lower  end  with  vegetable  parchment.  Fit 
a  bar  of  pure  zinc,  about  10  cm.  long,  tightly  into  a  cork 
which  just  closes  the  top  of  this  glass  tube.  Fill  the 
glass  tube  with  some  of  the  same  solution  of  potassium 
sulphate,  and  insert  the  bar  of  zinc  —  the  cork  closing 
the  top  of  the  glass  tube.  Around  the  top  of  the  zinc 
bar  above  the  cork  wrap  a  piece  of  platinum  wire  of 
sufficient  length  to  reach  nearly  to  the  bottom  of  the 
beaker,  when  the  glass  tube  is  introduced  into  the  beaker 
in  the  manner  to  be  hereafter  described.  The  free  end 
of  the  platinum  wire  should  be  coiled  upon  itself  a  num- 


APPLICATIONS  OF  THE  THEORY  263 

her  of  times,  or  it  is  better  if  it  is  connected  with  a  piece 
of  platinum  foil  a  few  centimetres  square,  so  as  to  expose 
a  larger  surface. 

The  glass  tube  is  now  immersed  in  the  beaker  until  the 
surface  of  the  solution  in  the  tube  is  only  a  centimetre  or 
two  above  the  surface  of  the  solution  in  the  beaker,  the 
free  end  of  the  platinum  wire,  or  the  platinum  foil,  being 
allowed  to  rest  on  the  bottom  of  the  beaker. 

If  a  few  drops  of  sulphuric  acid  are  introduced  into  the 
potassium  sulphate  just  around  the  bar  of  zinc,  the  zinc 
will  be  very  slightly  affected.  But  if  a  few  drops  of  sul- 
phuric acid  are  poured  upon  the  coiled  end  of  the  platinum 
wire,  or  upon  the  platinum  foil,  the  zinc  will  dissolve 
rapidly  in  the  neutral  potassium  sulphate  which  surrounds 
it,  and  a  copious  evolution  of  hydrogen  will  take  place 
from  the  platinum,  where  it  is  in  contact  with  the  sulphuric 
acid.  After  a  few  moments  the  presence  of  zinc  can  be 
demonstrated  in  the  inner  tube,  by  any  of  the  well-known 
reactions  for  zinc. 

As  Ostwald  states,  similar  phenomena  have  long  been 
known.  Nearly  forty  years  ago  Thomsen  l  described  a 
galvanic  element,  which  consists  of  copper  in  dilute  sul- 
phuric acid,  and  carbon  in  a  chromate  mixture.  When  the 
carbon  and  copper  were  connected,  the  metal  dissolved  as 
the  sulphate,  in  sulphuric  acid,  in  which  copper  alone  is 
not  soluble.  While  similar  facts  were  known,  there  was 
no  rational  explanation  offered  to  account  for  them,  until 
Arrhenius  proposed  the  Theory  of  Free  Ions. 

It  is  almost  self-evident  that  the  phenomenon  is  closely 
connected  with  electrical  changes.  Ostwald  demonstrated 

1  Pogg.  Ann.,  in,  192  (1860). 


264  ELECTROLYTIC   DISSOCIATION 

this,  by  introducing  between  the  metal  and  the  platinum  a 
fairly  sensitive  galvanoscope.  When  the  acid  was  added  to 
the  platinum,  the  presence  of  a  current  was  shown  by  the 
throw  of  the  instrument. 

The  explanation  of  this  phenomenon  is  perfectly  simple, 
now  that  we  have  the  theory  of  electrolytic  dissociation, 
and  are  familiar  with  its  application  to  the  primary  cell. 

When  metallic  zinc  is  immersed  in  a  solution  of  a  neutral 
salt,  like  potassium  sulphate,  it  sends,  in  consequence  of 
its  own  solution-tension,  a  certain  number  of  zinc  ions  into 
the  solution.  The  zinc  is  thus  made  negative,  and  the 
solution,  which  has  received  the  positive  ions,  positive. 
This  continues  until  a  definite  difference  in  potential  be- 
tween metal  and  solution  is  established.  The  amount  of 
metal  required  to  effect  this  condition  is,  as  we  have  seen, 
so  small  that  it  cannot  be  detected  by  any  chemical  means. 

The  zinc  cannot  dissolve  further,  because  of  the  excess 
of  positive  ions  in  the  solution.  In  order  that  more  zinc 
may  pass  into  solution,  some  of  these  positive  ions  must 
be  removed.  If  the  zinc  is  in  combination  with  another 
metal,  such  as  platinum,  the  latter  takes  the  same  nega- 
tive charge  as  the  zinc.  When  the  platinum  is  immersed 
in  the  solution,  it  attracts  the  excess  of  positive  ions  in 
the  solution,  and  these  collect  upon  the  platinum. 

We  would  expect  the  excess  of  positive  ions  in  the 
solution  to  give  up  their  charge  to  the  negative  platinum, 
and  separate  from  the  solution,  or,  in  case  of  potassium, 
decompose  the  water  which  is  present.  This  depends 
both  upon  the  nature  of  the  ion  and  of  the  electrode.  If 
the  positive  ion  is  the  potassium  of  potassium  sulphate, 
the  difference  in  potential  produced  by  introducing  the 


APPLICATIONS  OF  THE  THEORY  265 

zinc  is  not  sufficient  to  cause  this  ion  to  lose  its  charge 
to  the  platinum.  If  sulphuric  acid  is  added  to  the 
platinum,  the  difference  in  potential,  produced  by  intro- 
ducing the  bar  of  zinc,  is  sufficient  to  compel  the 
hydrogen  to  give  up  its  positive  charge  to  the  platinum, 
and  separate  as  ordinary  hydrogen.  The  platinum,  having 
received  positive  electricity  from  the  hydrogen  ions,  con- 
ducts this  over  to  the  zinc.  The  zinc  becomes  less  nega- 
tive than  before  the  hydrogen  separated  at  the  platinum, 
and  the  difference  in  potential  between  the  zinc  and 
the  surrounding  solution  is  less  than  before.  More  zinc 
dissolves  or  passes  over  into  ions,  more  hydrogen  ions 
give  up  their  charge  to  the  platinum  and  separate  as 
gas ;  and  this  continues  until  all  of  the  zinc  has  dissolved, 
or  all  of  the  hydrogen  ions  have  separated  as  gas. 

As  Ostwald  observes,  this  explanation  shows  not  only 
why  the  acid  must  be  added  to  the  platinum  and  not 
to  the  zinc,  but  throws  light  also  on  the  problem  of  the 
solution  of  metals  in  general.  A  word  or  two  on  this 
subject.  It  has  long  been  known  that  pure  zinc  does 
not  dissolve  in  acids,  while  impure  zinc  readily  dissolves. 
It  is  quite  evident  that  the  zinc  in  the  two  cases  has 
the  same  tendency  to  dissolve.  Pure  zinc  dissolves  readily 
when  in  contact  with  a  metal,  such  as  platinum,  which  has 
a  small  solution-tension.  As  we  have  seen  from  the  fore- 
going explanation,  the  difference  is  not  in  the  solution 
of  the  zinc,  but  in  the  ease  with  which  the  hydrogen 
can  escape  from  the  solution.  The  presence  of  a  metal 
with  small  solution-tension  allows  this  to  take  place  more 
readily,  and  this  is  the  reason  that  impure  zinc  dissolves 
in  acids. 


266  ELECTROLYTIC  DISSOCIATION 

The  reason  why  pure  zinc  does  not  dissolve  in  acids  is 
because  this  metal  has  a  strong  positive  solution-tension ; 
it  sends  positively  charged  ions  into  solution  under  a 
high  solution-tension,  and,  therefore,  opposes  the  separa- 
tion of  any  other  positive  ion,  like  hydrogen,  upon  it. 
Pure  zinc,  therefore,  does  not  dissolve  in  acids,  because  the 
hydrogen  ions  cannot  give  up  their  positive  charges  and 
escape. 

When  a  metal  like  platinum,  which  has  a  small  solution- 
tension,  is  present,  the  hydrogen  can  easily  give  up  its 
charge  to  this  metal  and  escape  as  gas.  The  zinc,  because 
of  its  high  solution-tension,  and  because  the  hydrogen 
cations  can  so  easily  escape,  then  dissolves. 

To  repeat  the  essential  steps  in  the  explanation  of  the 
experiment  described  above:  Pure  zinc  immersed  in  po- 
tassium (or  any  soluble)  sulphate,  to  which  sulphuric 
acid  is  added,  or  in  a  solution  of  pure  sulphuric  acid 
itself,  does  not  dissolve,  because  the  zinc  has  such  a  high 
solution-tension  that  the  hydrogen  ions  cannot  give  up 
their  charge  to  it  and  escape.  The  zinc,  however,  throws 
a  few  ions  into  solution,  and  becomes  negatively  charged. 
If  now  the  zinc  is  connected  with  platinum,  which  has 
a  small  solution-tension,  and  the  acid  added  to  the  plati- 
num, the  hydrogen  ions  can  easily  give  up  their  charge 
to  the  platinum  and  escape  as  gas.  The  platinum,  which 
was  at  the  potential  of  the  zinc  with  which  it  is  in  com- 
bination, now  becomes  positive  with  respect  to  the  zinc, 
and  a  positive  charge,  therefore,  flows  from  the  platinum 
to  the  zinc.  The  zinc,  having  received  positive  electricity, 
can  begin  dissolving  anew,  and  continue  to  pass  into 
solution  as  long  as  it  receives  positive  electricity  from 


APPLICATIONS  OF  THE  THEORY  267 

the  platinum  —  as  long,  therefore,  as  there  are  any  hydro- 
gen ions  in  the  solution  to  furnish  positive  electricity  to 
the  platinum.  Or,  as  we  are  accustomed  to  express 
it,  as  long  as  there  is  any  acid  in  contact  with  the 
platinum. 

This  subject  will  be  concluded  with  a  paragraph  from 
this  fascinating  paper  by  Ostwald :  "  We  see  that  the 
usual  explanation,  that  solution  takes  place  because  of 
galvanic  currents  between  the  zinc  and  the  other  metals, 
is  not  in  strict  accord  with  the  facts.  The  galvanic 
currents  are  inseparably  connected  with  the  process 
of  solution,  but  they  are  not  the  primary  causes  of  the 
solution.  They  are  set  up,  rather,  by  the  process  of  solu- 
tion, which  they  must  necessarily  accompany,  since  solu- 
tion is  a  question  of  ion  formation  and  disappearance. 
If  it  is  possible  for  the  positive  ions  present  to  separate 
in  any  way  from  the  solvent,  solution  takes  place." 

Ostwald  then  goes  on  to  show  that  it  is  not  necessary 
for  the  ion  to  separate  from  the  solution.  The  positive  ion 
may  be  destroyed  in  the  solution,  or  a  negative  ion  pro- 
duced; and  in  either  case  the  metal  will  dissolve.  But 
for  these  and  similar  facts  the  original  paper  must  be 
consulted. 

Conclusion.  —  In  concluding  this  chapter  on  the  calcula- 
tion of  the  electromotive  force  of  elements,  attention  should 
again  be  called  to  the  fact,  that  the  method  worked  out  by 
Nernst  was  based  directly  upon  van't  Hoff's  laws  of 
osmotic  pressure,  and  the  theory  of  electrolytic  dissocia- 
tion. Without  either  of  these  conceptions  the  work  of 
Nernst  would  have  been  absolutely  impossible.  With 
them,  he  has  thrown  entirely  new  light  on  the  whole  ques- 


268  ELECTROLYTIC   DISSOCIATION 

tion  of  the  electromotive  force  of  elements,  and  has  fur- 
nished us,  for  the  first  time,  with  a  satisfactory  theory  of 
the  action  of  the  primary  cell. 

APPLICATION    OF    THE    THEORY    OF    ELECTROLYTIC    DISSOCIA- 
TION  TO    BIOLOGICAL    PROBLEMS 

The  application  of  a  theory  of  solution  to  biological 
problems  is  not  so  evident  as  to  chemical,  where  solutions 
are  always  involved.  Solutions  are,  however,  very  fre- 
quently used  by  the  physiologist,  and  any  theory  of 
solution  must,  therefore,  bear  upon  many  physiological 
problems. 

It  is  only  in  the  last  few  years  that  the  theory  of  electro- 
lytic dissociation  has  found  its  way  into  physiology,  and 
•work  along  this  line  may  be  said  to  have  just  been  begun. 
A  few  examples  of  the  application  of  the  theory  in  this 
direction  will  be  given. 

Toxic  Action  and  Electrolytic  Dissociation.  —  Kahlenberg 
and  True1  published  a  paper  in  1896  on  "The  Toxic 
Action  of  Dissolved  Salts  and  their  Electrolytic  Dissocia- 
tion," which  was  the  pioneer  work  along  this  line. 

It  had  been  thought  that  the  physiological  action  of  any 
substance  was  due  to  its  chemical  nature.  In  the  case  of 
a  solution,  all  of  the  chemical  and  physical  properties  are 
a  function  of  the  properties  of  the  ions,  plus  those  of  the 
undissociated  molecules  which  it  contains.  It  would,  there- 
fore, seem  probable,  that  the  physiological  action  of  such 
solutions  was  due  to  the  same  cause.  Many  investigations 
on  the  physiological  action  of  aqueous  solutions  on  bacteria 
and  higher  forms  of  plant  life,  as  well  as  on  animals,  have 

1  Botan.  Gazette,  22,  81. 


APPLICATIONS   OF  THE  THEORY  269 

been  made.  In  work  of  this  kind,  percentage  concentra- 
tion has  been  dealt  with,  and  this  obscures  any  general 
relations  which  might  exist. 

If  a  dilute  solution  of  sodium  chloride  differs  from  a 
dilute  solution  of  hydrochloric  acid,  in  that  the  former 
contains  sodium  ions  and  the  latter  hydrogen  ions,  then: 
the  poisonous  character  of  the  latter  must  be  due  to 
the  hydrogen  ions. 

Since  a  very  dilute  solution  is  completely  dissociated, 
the  poisonous  properties  of  such  a  solution  must  be  due  to 
one  or  both  of  the  ions  which  it  contains,  since  there  are 
no  molecules  present.  If  the  toxic  action  of  acids  on 
plants  is  due  only  to  the  hydrogen  ion,  then  solutions  of 
different  acids  containing  the  same  number  of  hydrogen 
ions  should  be  equally  poisonous.  Solutions  of  hydro- 
chloric acid,  nitric  acid,  and  sulphuric  acid  are  completely 
dissociated  at  a  volume  of  about  one  thousand  litres; 
hence,  solutions  of  these  acids  which  are  of  this  strength, 
or  more  dilute,  should  have  the  same  toxic  action ;  since  the 

ions  Cl,  NO3,  SO4,  have  none. 

This  has  been  tested,  experimentally,  for  the  higher 
plants,  by  finding  the  strength  of  the  solution  of  the  acid 
in  which  the  root  of  the  plant  will  just  live.  Seedlings  of 
Lupinus  albus  L.  were  employed.  They  have  a  straight, 
clean  radicle,  and  are  well  adapted  to  this  work.  The 
root  was  suspended  in  the  acid  solution,  and  its  condition 
determined  by  the  rate  of  growth.  It  was  a  simple  matter 
to  determine  when  the  root  was  dead,  since  it  lost  its  satiny 
lustre  and  acquired  a  dead-white  color.  Its  appearance 
may  be  described  as  coagulated.  The  root  was  immersed 
in  the"  solution  for  fifteen  to  twenty-four  hours,  which  was 


270  ELECTROLYTIC  DISSOCIATION 

the  time  chosen  for  an  experiment.  The  root  of  the  plant 
was  first  placed  in  a  more  concentrated  solution  of  the 
acid.  If  this  was  found  to  kill  it,  another  root  was  placed 
in  a  more  dilute  solution,  and  so  on,  until  a  dilution  was 
reached  in  which  the  root  just  lived.  In  the  case  of  strong 
acids,  the  root  would  just  live  in  a  solution  which  contained 
a  gram-molecular  weight  of  the  acid  in  6400  litres  of  solu- 
tion; expressed  in  ordinary  terms,  the  solution  had  a 
volume  of  6400  litres.  This  expresses  the  toxic  action  of 
the  hydrogen  ion,  and  it  is  the  same  for  all  strong  acids. 
The  hydroxyl  ion  was  studied,  and  found  to  be  far  less 
poisonous  than  the  hydrogen  ion.  The  root  would  just 
live  when  the  solution  contained  a  gram-molecular  weight 
of  the  base  in  400  litres  of  solution.  The  effect  of  the 
ions  of  certain  salts  was  also  studied.  The  copper  ion 
was  especially  toxic.  The  roots  would  just  survive  in  a 
solution  which  contained  a  gram-molecular  weight  of 
copper  ions  in  51,200  litres  of  solution. 

Whenever  copper  forms  part  of  an  ion,  and  is  not  the 
whole  ion,  the  result  is  very  different.  Thus,  in  Fehling's 
solution  copper  forms  part  of  the  ion,  it  being  in  com- 
bination with  an  organic  complex.  We  would  expect  it, 
therefore,  to  have  a  different  action,  under  these  condi- 
tions, than  when  alone.  This  was  tested  by  experiment. 
In  preparing  the  Fehling's  solution,  cane-sugar  was  used 
instead  of  Rochelle  salt,  in  order  to  avoid  the  excess  of 
other  ions  in  the  solution.  An  excess  of  caustic  alkali 
was  avoided,  in  order  to  keep  out  hydroxyl  ions,  which 
are  known  to  be  poisonous.  The  roots  would  grow  in  a 
solution  of  this  salt,  which  contained  a  gram-atomic  weight 
of  copper  in  400  litres.  Copper,  when  alone  as  an  ion,  is, 


APPLICATIONS   OF  THE  THEORY  271 

thus,  far  more  poisonous  than  when  in  combination  with 
this  complex. 

Iron  in  its  ionic  state  has  very  different  toxic  action 
than  when  the  iron  atom  is  combined  with  other  things  to 
form  an  ion.  Thus  the  iron  in  a  ferric  salt  has  very 
different  effect  from  the  iron  in  potassium  ferrocyanide. 
It  would  be  indeed  surprising  if  this  were  not  true,  since 
iron  in  a  ferric  salt  forms  a  cation,  while  iron  in  potassium 
ferrocyanide  is  combined  with  the  6  CN  groups,  forming  a 
part  of  the  complex  anion. 

Cobalt  and  nickel  have  the  same  toxic  action  as  iron. 
The  question  is  raised,  whether  there  is  any  connection 
between  this  action  and  the  fact  that  the  three  elements 
have  very  nearly  the  same  atomic  weights.  The  experi- 
mental data  are  yet  far  too  meagre  to  answer  this  ques- 
tion. Cadmium  and  silver  also  are  found  to  be  very 
poisonous. 

The  Cu  ion  is  about  as  toxic  as  the  hydrogen  ion. 
Hydrocyanic  acid  is  almost  completely  undissociated,  yet 
it  is  very  poisonous.  The  plant  will  stand  only  T^|-o~o  °^  a 
gram-molecule  per  litre.  This  is  an  excellent  example  of 
how  molecules  as  well  as  ions  may  be  poisonous. 

The  investigation  was  extended  to  the  organic  acids,  and 
these,  with  some  exceptions,  fell  in  line  with  the  above 
relations. 

This  investigation  has  shown  that  the  toxic  action  of 
solutions  of  electrolytes,  which  are  completely  dissociated, 
is  due  to  the  ions  present.  When  the  electrolyte  is  only 
partly  dissociated,  the  undissociated  portion  may  exert  a 
toxic  action.  We  have  here  a  recognition  of  the  theory  of 
electrolytic  dissociation  in  the  organic  world.  The  paper 


2/2  ELECTROLYTIC  DISSOCIATION 

of  Kahlenberg  and  True  contains  the  following  significant 
passage :  — 

"  It  will  be  seen  that  a  wide  field  for  research  along 
physiological  lines  opens  up,  by  applying  to  the  field  of 
biology  the  dissociation  theory  which  has  proved  so  fertile 
in  chemistry  and  physics.  Further  work  in  this  direction, 
using  the  latest  and  best  that  the  new  physical  chemistry 
has  to  offer,  it  is  to  be  hoped,  will  place  our  knowledge  of 
the  physiological  action  of  solutions  of  electrolytes  on  a 
better  basis  than  the  purely  empirical  one  on  which  it  has 
thus  far  rested.  It  does  not  seem  too  much  to  expect  that 
the  effect  of  such  study  will  soon  be  felt  in  agriculture  and 
therapeutics,  while  bacteriological  study,  pursued  from  the 
standpoint  of  the  new  theory,  will  yield  important  additions 
to  our  knowledge  of  antiseptics." 

Another  investigation  in  the  same  field  has  been  carried 
out  by  F.  D.  Heald.1  He  studied  the  toxic  action  of 
acids  and  salts  upon  different  plants.  He  used  the  three 

plants : — 

Pisum  sativum, 

Zea  Mais, 
Cucurbita  Pepo. 

The  conclusions  of  Kahlenberg  were  all  confirmed  by 
this  work,  in  which  more  than  one  plant  was  used.  Says 
the  author,  "The  theory  of  electrolytic  dissociation  has 
thus  thrown  light  upon  the  physiological  action  of  different 
substances,  and  the  theory  has,  itself,  been  strengthened 
by  these  experiments  upon  living  things." 

Toxic  Action  of  the  Phenols  and  their  Dissociation.  — 
The  work  begun  by  Kahlenberg  and  True  has  since  been 

1  Botan.  Gazette,  22,  125. 


APPLICATIONS  OF  THE  THEORY  2/3 

extended  by  True  and  Hunkle1  to  the  phenols.  They 
investigated  a  number  of  phenols,  using  different  con- 
centrations, and  determined  the  greatest  concentration 
in  which  the  roots  of  Lupinus  albus  would  just  live  and 
grow.  The  conductivity  of  the  solutions  of  the  different 
phenols  was  also  measured.  They  conclude  that,  except  in 
isolated  instances,  the  electrolytic  dissociation  plays  but  a 
subordinate  rdle  in  determining  the  toxic  properties  of 
phenylic  compounds.  Picric  and  salicylic  acids  are  strongly 
dissociated,  and  are  very  poisonous  because  of  the  large 
number  of  hydrogen  ions  in  their  solutions.  Electrolytic 
dissociation  exerts  a  pronounced  influence  in  the  cresols 
and  mononitrophenols. 

Dissociation  and  Disinfecting  Action.  —  In  1896  a  paper 
appeared  by  Paul  and  Kronig,2  describing  the  action  of  a 
large  number  of  reagents  on  bacteria.  The  work  was  done 
chiefly  with  the  bacillus  anthracis,  and  the  staphylococcus 
pyogenes  aureus.  As  will  be  seen,  the  problem  is  one  of 
disinfection,  the  toxic  action  of  the  various  substances 
being  investigated.  The  bacteria  were  distributed  over 
the  surfaces  of  carefully  washed  and  completely  disin- 
fected garnets  of  equal  size.  That  approximately  the 
same  number  of  bacteria  should  be  used  in  each  experi- 
ment, the  same  number  of  garnets  was  employed,  and 
the  mean  of  six  results  was  taken.  The  garnets  were 
placed  in  vessels  made  of  platinum  gauze,  and  introduced 
into  the  solution,  which  was  kept  at  a  constant  tempera- 
ture. After  the  action  had  taken  place  as  long  as  desired, 
it  was  instantly  brought  to  an  end  by  adding  some  sub- 

1  Botan.  Centralb.,  76,  289,  321,  361,  391  (1898). 

2  Ztschr.  phys.  Chem.,  21,  414. 


2/4  ELECTROLYTIC  DISSOCIATION 

stance  which  destroyed  the  disinfecting  property  of  the 
solution.  The  spores  were  then  washed  from  the  garnets 
by  shaking  in  water,  and  agar-agar  jelly  added  to  the 
water  containing  the  spores.  This  mixture  was  poured 
into  convenient  dishes,  and  kept  at  a  constant  temperature. 
The  bacteria,  which  were  still  alive,  began  to  form  dis- 
tinctly visible  colonies  in  twenty-four  hours,  and  could 
easily  be  counted.  The  number  of  colonies  was  found  to 
depend  upon  the  time  during  which  the  toxic  reagent 
acted,  and  upon  the  concentration  of  the  solution.  In 
general,  the  more  dilute  the  solution  the  less  the  dis- 
infecting action.  The  nature  of  the  solvent  was  found  to 
effect  the  relative  toxic  action  of  compounds. 

Some  of  the  more  important  results  obtained  by  Paul 
and  Kronig  are  :  — 

The  disinfecting  action  of  metallic  salts  depends,  not 
only  on  the  concentration  of  the  metal  in  the  solution,  but 
also  on  the  specific  properties  of  the  salt  and  the  solvent. 

The  action  of  a  salt  of  a  metal  depends  not  only  on  the 
specific  action  of  the  metallic  ion,  but  also  on  that  of  the 
anion,  and  of  the  undissociated  part  of  the  salt. 

Solutions  of  metallic  salts,  in  which  the  metal  forms  part 
of  a  complex  ion,  are  only  weakly  disinfecting. 

The  strong  acids  are  toxic,  not  only  in  proportion  to  the 
concentration  of  the  hydrogen  ions,  but  the  specific  prop- 
erties of  the  anions  come  into  play.  The  bases  which  are 
equally  dissociated,  such  as  potassium,  sodium,  and  lithium 
hydroxides,  have  the  same  disinfecting  action.  The 
weakly  dissociated  base,  ammonium  hydroxide,  disinfects 
much  less. 

The  disinfecting  action  of  the  halogens,  Cl,  Br,  I,  like 


APPLICATIONS  OF  THE  THEORY  2/5 

their  chemical  action,  decreases  with  increasing  atomic 
weight. 

Solutions  of  substances  in  absolute  alcohol  and  ether 
are  almost  without  action  on  bacillus  anthracis. 

The  disinfecting  action  of  mercuric  chloride  and  silver 
nitrate  in  alcohol  is  increased  by  the  addition  of  more 
and  more  water. 

These  results  are  very  interesting,  as  being  an  applica- 
tion of  the  theory  of  electrolytic  dissociation  in  an  entirely 
new  direction.  We  have  here  a  clear  recognition  of  dis- 
sociation in  the  field  of  bacteriology. 

Toxic  Action  of  Substances  on  Certain  Fungi. — We  have 
seen  the  relation  between  the  dissociation  of  solutions  and 
their  toxic  action  on  certain  phanerogams,  as  brought  out 
by  the  work  of  Kahlenberg,  True,  and  Heald ;  also  the 
same  relation  when  lower  forms  of  life,  the  bacteria,  were 
used.  We  must  refer,  in  this  connection,  to  the  very  recent 
investigation  of  Clark,  in  which  the  toxic  action  of  sub- 
stances on  certain  fungi  was  studied,  and  this  action  com- 
pared with  the  dissociation  of  the  substance.  Five  fungi 
were  used,  and  all  were  found  to  be  much  more  resistant  to 
injurious  agents  than  the  higher  plants.  The  spores  of 
moulds  require,  to  inhibit  germination,  from  two  to  four 
hundred  times  the  strength  of  acid  which  is  fatal  to  the 
higher  plants.  The  hydroxyl  ion  was  found  to  be  more 
toxic  to  moulds  than  the  hydrogen  ion.  The  toxic  value  of 
the  ions,  Cl,  Br,  I,  increases  with  increasing  atomic  weight. 
It  was  found  that  in  the  case  of  several  acids  dissociation 
lessens  their  activity,  the  molecule  being  more  active  than 
the  ions.  Of  the  eight  acids  investigated,  six  were  more 
active  in  the  molecular  than  in  the  ionic  form.  The  toxic 


276  ELECTROLYTIC  DISSOCIATION 

action  of  the  molecule,  in  the  case  of  hydrocyanic  acid, 
was  as  much  as  76.6  times  that  of  the  hydrogen  ion.  The 
anions  of  hydrochloric,  nitric,  and  sulphuric  acids  are  only 
slightly  toxic  to  fungi. 

These  results,  like  those  previously  described,  show  that 
both  molecules  and  ions  may  be  poisonous  to  certain  forms 
of  life,  just  as  both  molecules  and  ions  may  be  colored. 
The  poisonous  nature  of  the  molecule  or  ion  depends 
greatly  upon  the  nature  of  the  plant  on  which  it  acts. 

Application  of  the  Dissociation  Theory  to  Animal  Phys- 
iology. —  The  theory  of  electrolytic  dissociation  has  been 
applied  not  only  to  vegetable,  but  has  already  found  its 
way  into  animal  physiology.  The  work  of  Loeb1  was 
the  first  of  importance  in  this  field.  He  studied 
the  action  of  certain  electrolytes  on  the  muscle  of  a 
frog.  When  the  muscle  from  the  leg  of  a  frog  is  placed 
in  a  0.7  per  cent  solution  of  sodium  chloride,  and  a 
small  amount  of  acid  or  base  added  to  the  solution,  the 
muscle,  by  taking  up  water,  undergoes  an  appreciable 
increase  in  weight.  Loeb  determined  the  increase  in  the 
weight  of  the  muscle,  produced  by  hydrochloric  acid, 
nitric  acid,  and  sulphuric  acid,  of  known  concentrations, 
and  was  led  to  this  interesting  conclusion.  Solutions  of 
these  three  acids,  which  contain  the  same  number  of 
hydrogen  atoms  in  equal  volumes,  produce  the  same  in- 
crease in  the  weight  of  the  muscle.  He  showed  that  it  is 
only  the  hydrogen  cation  which  is  active,  the  anion  having 
little  or  no  effect;  and  that  when  the  same  number  of 
hydrogen  ions  is  contained  in  equal  volumes  of  their  solu- 
tions, all  of  these  acids  produce  exactly  the  same  effect. 

1  Pfltiger's  Archiv  f.  Physiologic,  69, 1. 


APPLICATIONS  OF  THE  THEORY 

This  does  not  hold  for  the  weakly  dissociated  organic 
acids,  since,  in  these  cases,  the  anions  as  well  as  the  mole- 
cules exert  an  influence.  Loeb  then  studied  the  action 
of  the  following  bases :  lithium  hydroxide,  sodium  hy- 
droxide, potassium  hydroxide,  strontium  hydroxide,  and 
barium  hydroxide,  and  found  that  they  all  had  the  same 
influence  in  causing  the  muscle  to  take  up  water,  when 
they  are  used  at  such  concentrations  that  an  equal  number 
of  hydroxyl  groups  is  contained  in  equal  volumes  of  each 
of  the  solutions.  The  action  of  all  these  alkalies  was 
found  to  depend  entirely  upon  the  anion  of  the  base,  i.e. 
hydroxyl;  just  as  the  action  of  the  strong  mineral  acids 
depended  entirely  upon  the  cation  hydrogen.  The  hy- 
droxyl ions  have,  however,  a  stronger  influence  than  an 
equal  number  of  hydrogen  ions.  Solutions  of  potassium 
and  sodium  carbonate  also  cause  the  muscle  to  take  up 
water.  This  is  due  to  the  hydroxyl  ions  in  their  solutions, 
formed  by  the  hydrolysis  of  the  salt  and  the  subsequent 
dissociation  of  the  base. 

That  the  theory  of  osmotic  pressure,  deduced  by  van't 
Hoff,  applies  to  this  phenomenon,  is  shown  by  the  fact 
that  solutions  of  lithium,  potassium,  rhubidium,  caesium, 
magnesium,  calcium,  barium,  and  strontium  chlorides, 
produce  the  same  change  in  the  weight  of  the  muscle 
as  a  solution  of  sodium  chloride  of  equal  osmotic 
pressure. 

Loeb  also  studied  the  toxic  action  of  a  number  of  ions 

+      + 

on  muscle,  and  found  that  for  any  given  group,  as  Li,  Na, 
+      +"    + 
K,  Rb,  Cs,  the  relative  toxic  action  is  proportional  to  the 

migration  velocity  of  these  ions,  and  not  to  their  atomic 


2/8  ELECTROLYTIC  DISSOCIATION 

++    +  + 

weights.     The  same  relation  obtains  for  the  ions,  Be,  Mg, 

Ca,  Ba,  Sr,  but  does  not  extend  from  one  natural  group  of 
the  elements  to  another. 

A  second  investigation  was  carried  out  by  Loeb,1  which 
is  an  extension  of  the  one  just  considered.  While  the 
physiological  action  of  the  inorganic  acids  is  conditioned 
by  the  number  of  hydrogen  ions  present,  there  is  an 
apparent  exception  presented  by  the  organic  acids.  The 
physiological  activity  of  the  fatty  acids  is  not  proportional 
to  their  dissociation.  Thus,  lactic  acid,  which,  at  the  dilu- 
tion employed  is  only  eleven  per  cent  dissociated,  causes 
the  muscle  to  take  up  as  much  water  as  trichloracetic  acid 
and  oxalic  acid,  in  which  nearly  all  of  the  molecules  are 
dissociated.  Similarly,  mandelic  acid  causes  the  muscle  to 
take  up  as  much  water  as  the  more  strongly  dissociated 
organic  acids,  although,  at  the  dilution  used,  it  is  only  nine- 
teen per  cent  dissociated.  Loeb  does  not  offer  any  final 
explanation  of  this  phenomenon,  but  suggests  that  since 
the  difference  in  the  action  of  the  different  acids  is  so 
much  less  than  the  difference  in  their  dissociation,  it 
seems  probable  that  those  acids  which  are  very  slightly 
dissociated  are  transformed  in  the  muscle  into  products 
with  stronger  dissociation.  The  author  offers  this  as  a 
possible  explanation,  and  promises  further  investigation, 
especially  with  the  aromatic  acids. 

Physical  Chemical  Methods  applied  to  Animal  Physi- 
ology. —  Physical  chemical  methods  have  been  applied  by 
Bugarszky  and  Tangl2  to  a  very  different  physiological 
problem.  They  have  been  employed  to  determine  the  con- 

1  Pfliiger's  Archiv  f.  Physiologic,  71,  457.  Ibid.,  72,  531. 


APPLICATIONS  OF  THE  THEORY  2/9 

centration  of  the  dissolved  substances  in  the  blood  serum, 
and  also  the  relation  between  the  electrolytes  and  non- 
electrolytes  contained  in  it. 

The  freezing-point  method  was  used  to  determine  the 
molecular  concentration  of  the  dissolved  substances.  The 
freezing-point  of  the  serum  was  first  determined,  then 
the  freezing-point  of  pure  water.  Since  blood  serum  is 
practically  water  containing  electrolytes  and  non-electro- 
lytes, the  difference  between  the  two  freezing-points  is  the 
lowering  of  the  freezing-point  of  water  produced  by  the 
substances  present  in  the  blood  serum.  A  gram-molecular 
solution  of  a  non-electrolyte  freezes  1.87°  lower  than  pure 
water.  To  determine,  therefore,  the  number  of  gram- 
molecular  concentrations  to  which  the  substances  in  blood 
serum  are  equivalent,  the  difference  between  the  freezing- 
point  of  water  and  of  blood  serum  must  be  divided  by 
1.87.  In  this  calculation  the  ions  which  result  from  the 
dissociation  of  any  electrolytes  present  are  treated  as  if 
they  were  molecules,  since  an  ion  produces  the  same  low- 
ering of  the  freezing-point  as  a  molecule. 

The  above  method  shows  the  total  concentration  of  elec- 
trolytes and  non-electrolytes  present  in  blood  serum,  but 
does  not  enable  us  to  determine  the  amount  of  each.  To 
accomplish  this,  some  method  must  be  employed  which  will 
enable  us  to  discriminate  between  undissociated  molecules 
and  ions.  Molecules  in  solution  do  not  conduct  the  elec- 
tric current ;  only  ions  conduct.  We  can,  therefore,  use  the 
conductivity  method  to  determine  the  amount  of  electro- 
lytes present  in  the  serum.  This  was  done  by  Bugarszky 
and  Tangl.  The  electrolytes  present  in  blood  serum  are, 
almost  all,  salts.  The  alkaline  reaction  of  the  blood  comes 


280  ELECTROLYTIC  DISSOCIATION 

from  a  few  hydroxyl  ions,  which  result  from  the  hydro- 
lysis of  carbonates  in  the  blood.  Further,  the  salts  in  the 
blood  are  nearly  all  inorganic ;  organic  salts  being  present 
only  in  very  small  quantity.  The  conductivity  method 
is  used  as  an  approximate  measure  of  the  inorganic 
salts  present,  and  is  regarded  as  more  accurate  than  the 

method  of  determining  the  amount  of  ash  obtained  from 

+      + 
the  serum.     While  the  serum  contains  the  cations,  Na,  K, 

Ca,  Mg,  and  the  anions  Cl,  CO3,  HCO3,  HPO4,  SO4,  O~H  ; 

+      —  = 

the  main  ions  are  Na,  Cl,  and  some  CO3. 

The  determination  of  the  concentration  of  the  electrolytes 
in  the  blood  serum,  by  the  conductivity  method,  is  some- 
what complicated  by  the  presence  of  the  non-electrolytes 
in  the  serum,  as  the  authors  point  out.  The  conductivity 
of  an  electrolyte  is  diminished  by  the  presence  of  a  non- 
electrolyte,  and  the  magnitude  of  the  effect  depends  both 
upon  the  nature  of  the  electrolyte  and  the  non-electrolyte. 
The  non-electrolytes  in  the  blood  serum  consist  chiefly 
of  albumens,  with  traces  of  a  number  of  other  substances. 
The  albumens  were  isolated,  and  their  effect  on  the  con- 
ductivity determined.  One  gram  of  albumen  in  100  cubic 
centimetres  of  blood  serum,  diminished  the  conductivity 
2.5  per  cent.  By  applying  this  correction  to  the  observed 
conductivity  of  the  serum,  we  obtain  its  true  conductivity. 
The  corrected  conductivity  can  be  used  for  calculating  the 
concentration  of  the  electrolytes  dissolved  in  the  serum. 
Knowing  the  amount  of  the  electrolytes  in  the  serum,  it 
is  a  very  simple  matter  to  determine  the  amount  of  the 
non-electrolytes.  The  freezing-point  method  gives  the  sum 
of  the  two,  as  already  stated.  By  subtracting  from  the 


APPLICATIONS   OF  THE   THEORY  281 

sum  the  amount  of  the  electrolytes,  we  have  at  once  the 
quantity  of  the  non-electrolytes. 

A  number  of  conclusions  of  interest  and  importance 
were  reached  through  this  work,  but  since  these  lie  almost 
wholly  in  the  field  of  physiology,  they  do  not  come  within 
the  scope  of  this  book.  The  authors  point  out  that 
these  same  methods  can,  and  should  be  applied  to  other 
liquids  in  the  animal  body. 

Application  of  Osmotic  Pressure  and  Dissociation  to  the 
Mechanics  of  Secretion.  —  The  work  of  Dreser 1  illustrates 
the  application  of  van't  Hoff  s  laws  of  osmotic  pressure 
and  the  theory  of  electrolytic  dissociation,  to  the  mechanics 
of  secretion.  The  problem  is  to  calculate  the  work  done 
by  the  kidneys  in  secreting  urine.  This  is  accomplished 
by  determining  the  osmotic  pressure  of  the  blood  serum, 
and  also  that  of  the  urine.  There  is  no  direct  method  of 
measuring  osmotic  pressure,  which  is  of  general  applica- 
bility, so  that  an  indirect  method  must  be  employed.  The 
well-known  freezing-point  method  was  used,  and  from  the 
difference  in  the  freezing-point  of  the  serum  and  of  the 
urine,  the  difference  in  their  osmotic  pressures  was  cal- 
culated. If  the  volume  secreted  by  the  kidneys  is  taken 
into  account,  the  osmotic  work  done  by  the  kidneys  is 
ascertained.  And  if  we  note  the  time  during  which  the 
secretion  takes  place,  the  osmotic  work  done  by  the  kidneys 
can  be  expressed  in  C.G.S.  units. 

A  number  of  other  investigations  have  already  been 
carried  out,  in  which  the  theory  of  electrolytic  dissociation 
and  the  van't  Hoff  laws  of  osmotic  pressure  have  been 
applied  to  biological  problems.2  We  should  mention  es- 

1  Archiv  f.  experimentelle  Pathologic,  29,  301. 

2  1'br  a  fuller  discussion  of  this  question  see  the  admirable  book  by  Hamburger. 
Osmotischer  Druck  und  lonenlehre  (1902) . 


282  ELECTROLYTIC  DISSOCIATION 

pecially  the  work  of  Dreser,1  Hamburger,2  Hedin,3  Heiden- 
hain,4  van  Karanyi,5  and  van  Limbeck.6  But  the  investi- 
gations already  referred  to,  suffice  to  show  the  nature  of 
the  biological  questions  upon  which  modern  physical 
chemistry  is  throwing  light. 

It  would  seem  that  the  theory  of  electrolytic  dissocia- 
tion must  find  wide  application  in  pharmacology.  If 
chemical  action  is  due  mainly  to  ions,  it  is  very  probable 
that  the  pharmacological  action  of  many  chemical  sub- 
stances is  largely  ionic.  This  probability  is  increased, 
when  we  consider  how  many  electrolytes  are  used  in 
medicine,  and  that  they  are  either  taken  in  solution,  or 
pass  into  solution  in  the  fluids  of  the  body.  It  is  quite 
safe  to  predict,  that  many  interesting  and  important  results 
await  the  investigation  of  the  relation  between  the  dis- 
sociation of  drugs,  and  their  action  upon  the  human  body. 

CONCLUSION 

By  following  a  few  of  the  many  applications  of  the 
theory  of  electrolytic  dissociation  to  problems  in  chemistry, 
physics,  and  biology,  we  can  form  some  conception  of  its 
wide-reaching  significance.  The  examples  which  have 
been  taken  up  and  studied  are,  in  each  case,  a  few  chosen 
from  the  many.  And  if  so  much  has  been  done  in  the 
short  time  which  has  elapsed  since  the  theory  was  pro- 

1  Ztschr.  phys.  Chem.,  21,  108. 

2  Du  Bois'  Archiv,  1886,  476 ;  Virchow's  Archiv,  140,  539 ;  Centralb.  f.  Physi- 
ologic, 1893-94,  24. 

8  Skandinav.  Archiv  f.  Physiologic,  5,  238,  385;  Pfliiger's  Archiv  f.  Physiologic, 
68,  248. 

4  Pfliiger's  Archiv,  56,  600. 

6  Centralb.  f.  Physiologic,  1893,  Heft  3  '<  Ungar.  Archiv  f.  Med.,  1895. 

6  Archiv  f.  exper.  Pathologic,  25,  64. 


APPLICATIONS  OF  THE  THEORY  283 

posed,  what  may  we  not  reasonably  expect  from  the 
future  ?  Since  so  many  substances  are  broken  down  into 
ions,  by  water  and  similar  solvents,  it  is  almost  certain  that 
our  theory  will  find  application  wherever  aqueous  solutions 
of  electrolytes  are  employed.  A  moment's  reflection  will 
show  that  comparatively  few  branches  of  natural  science 
lie  wholly  without  its  scope. 

A  careful  study  of  the  applications  of  the  theory,  which 
have  already  been  made,  will  bring  out  a  fact  of  pro- 
found significance.  The  theory  coordinates  and  corre- 
lates heterogeneous  masses  of  facts,  which  apparently 
bore  little  or  no  relation  to  one  another,  and  refers  them 
to  a  common  cause.  As  an  illustration,  take  the  neutrali- 
zation of  acids  and  bases,  or  the  strength  of  acids  and 
bases  in  general.  But  this  is  just  what  the  physical 
chemistry  of  to-day  has  done,  and  is  doing  for  several 
branches  of  science,  and  especially  for  the  science  of  chem- 
istry. Physical  chemistry  is  furnishing  us,  largely  with 
the  aid  of  the  theory  of  electrolytic  dissociation,  with 
rational  explanations  of  chemical  processes  whose  mean- 
ing was  entirely  concealed,  and  is  rapidly  placing  chem- 
istry upon  that  exact  mathematical  basis  which  physics 
has  so  long  enjoyed. 


INDEX 


Acids  and  bases,  strength  of,  216.    . 

Acids,  dry,  do  not  act  on  litmus,  165. 

Acidity,  relations  between,  and  composi- 
tion and  constitution,  219. 

Additive  nature  of  conductivity.  Law  of 
Kohlrausch,  116. 

Additive  property  of  salt  solutions,  104. 

Affinity,  methods  of  measuring,  67. 

Ammonia,  dry,  no  action,  on  dry  hydro- 
chloric acid,  168. 

Animal  physiology,  application  of  physi- 
cal chemical  methods  to,  278. 

Animal  physiology,  application  of  the  dis- 
sociation theory  to,  276. 

Arrhenius,  dissociation  of  substances  in 
water,  93. 

Arrhenius  explains  exceptions  to  gas 
laws,  94. 

Asymmetric  carbon  atom,  25. 

Atomic  and  molecular  volumes,  n. 

Avogadro's  law  for  dilute  solutions,  87. 

Baeyer  describes  an  exception  to  van't 

Hoff's  hypothesis,  24. 
Bases  and  acids,  strength  of,  216. 
Bases,  strength  of,  and  composition,  and 

constitution,  223. 
Benzene,  constitution  determined  by  a 

thermal  method,  21. 
Benzene,  constitution  determined  by  re- 

fractivity,  20. 
Bergmann,  work  of,  53. 
Berthelot  and  Pean  de  St.  Gilles,  work 

of,  58. 

Berthelot,  thermochemical  work  of,  34. 
Berthollet,  work  of,  54. 
Berzelius,  electrochemical  theory  of,  40. 
Biological  problems,  application  of  the 

theory  of  electrolytic  dissociation  to, 

268. 

Blagden,  on  freezing-point  lowering,  30. 
Boiling-points  and  composition,  5. 


Boiling-points  and  constitution,  5. 
Boiling-points  of  liquids,  4. 
Boiling-point  rise,  178. 
Boyle  and  Gay  Lussac's  laws  applied  to 
solutions.     Experimental  evidence  for, 

85- 

Boyle's  Law  confirmed  by  Pfeffer's  re- 
sults, 83. 

Boyle's  Law  confirmed  by  results  of  De 
Vries,  83. 

Boyle's  Law  for  dilute  solutions,  82. 

Bruhl,  on  refractive  power  of  liquids,  19. 

Calculation  of  dissociation  from  conduc- 
tivity, 209. 

Cell  for  measuring  osmotic  pressure,  74. 

Cells,  types  of,  238. 

Chatelier,  Le,  chemical  equilibrium,  66. 

Chemical  action  at  a  distance,  261. 

Chemical  action  at  a  distance,  demon- 
strated by  experiment,  262. 

Chemical  activity  as  a  measure  of  disso- 
ciation, 157. 

Chemical  dynamics  and  statics,  develop- 
ment of,  53. 

Chemical  problems,  electrolytic  dissocia- 
tion applied  to,  171. 

Chemical  reactions  between  ions,  158. 

Chlorine,  dry,  action  on  metals,  161. 

Clausius,  theory  of  electrolysis,  48. 

Cohen  and  van't  Hoff,  66. 

Color  of  salt  solutions,  no. 

Composition  and  acidity,  219. 

Composition  and  boiling-points,  5. 

Composition  and  heat  of  combustion,  37. 

Composition  and  magnetic  rotation,  28. 

Composition  and  molecular  heats,  8. 

Composition  and  refractivity,  18. 

Composition  and  strength  of  bases,  223. 

Concentration  and  osmotic  pressure,  75. 

Concentration  element  of  the  first  type, 
239- 


285 


286 


INDEX 


Concentration  element  of  the  second 
type,  243. 

Concentration  element,  sources  of  poten- 
tial, 252. 

Conductivity  and  dilution,  142. 

Conductivity  and  lowering  of  freezing- 
point,  129. 

Conductivity  and  osmotic  pressure,  128. 

Conductivity  and  reaction  velocity,  155. 

Conductivity  at  high  temperatures,  215. 

Conductivity  in  different  solvents,  211. 

Conductivity,  molecular,  203. 

Conductivity  of  solutions,  201. 

Conductivity  of  solutions,  Kohlrausch,  52. 

Conductivity  of  solutions,  method  of 
measuring,  203. 

Conductivity  of  water,  207. 

Conductivity,  specific,  202. 

Constancy  of  solution-tension,  236. 

Constitution  and  acidity,  219. 

Constitution  and  boiling-points,  5,  7. 

Constitution  and  heat  of  combustion,  37. 

Constitution  and  molecular  heats,  9. 

Constitution  and  molecular  volume,  12. 

Constitution  and  refractivity,  18. 

Dale  and  Gladstone,  refraction  formula, 

17- 
Daniell  elements,  electromotive  force  of, 

254- 

Davy,  electrochemical  theory  of,  40. 

Deville,  on  dissociation,  60. 

Diffusion,  174. 

Dilution  Law  of  Ostwald,  143. 

Dilution  Law  of  Rudolphi,  147. 

Disinfection  and  dissociation,  273. 

Dissociating  action  of  water,  demonstra- 
tion of,  113. 

Dissociating  power  of  different  solvents, 
160. 

Dissociation  and  chemical  activity,  154. 

Dissociation  by  heat  and  electrolytic  dis- 
sociation, 149. 

Dissociation  calculated  from  conduc- 
tivity, 209. 

Dissociation  measured  by  boiling-point 
method,  213. 

Dissociation  measured  by  different 
methods,  152. 

Dissociation  of  substances  in  water,  93. 

Distance,  chemical  action  at  a,  261. 


Distance,  chemical  action  at  a,  demon 

strated  by  experiment,  262. 
Dittmar,  on  boiling-points  of  metameric 

compounds,  6. 

Earlier  physical  chemistry,  i. 

Earlier  physical  chemical  work,  conclu- 
sions from,  69. 

Edwards,  refraction  formula,  17. 

Electrochemical  Theories  of  Davy  and 
Berzelius,  40. 

Electrochemistry  and  electrolytic  disso- 
ciation, 182. 

Electrochemistry,  the  development  of,  39. 

Electrolysis,  45,  183. 

Electrolysis,  theories  of,  46. 

Electrolytic  dissociation  and  dissociation 
by  heat,  149. 

Electrolytic  dissociation  and  toxic  action, 
268. 

Electrolytic  dissociation,  origin  of  the 
theory,  71. 

Electrolytic  dissociation,  theory  of,  94. 

Electrolytic  solution-tension,  231. 

Electromotive  force,  216. 

Electromotive  force,  calculated  from 
osmotic  pressure,  227. 

Electromotive  force,  seat  of  in  primary 
cells,  226. 

Electrostatically  charging  a  solution,  138. 

Elements,  concentration,  first  type,  239. 

Elements,  concentration,  second  type, 
243- 

Elements,  liquid,  247. 

Evidence  for  the  theory  of  electrolytic 
dissociation,  104. 

Exceptions  to  laws  of  gas  pressure  being 
applicable  to  osmotic  pressure,  91. 

Excess  of  one  of  the  products  of  disso- 
ciation, effect  of,  149. 

Faraday's  Law,  44. 

Favre  and  Silbermann,  thermochemical 

investigations,  33. 
Pick's  Law  of  diffusion,  30. 
Freezing-point,  lowering  of,  176. 
Fungi,  toxic  action  of  substances  on,  275. 

Gas-battery,  256. 

Gas  pressure  and  osmotic  pressure,  rela- 
tions, 76. 


INDEX 


287 


Gay  Lussac's  Law  and  Boyle's  Law,  ex- 
perimental evidence  for,  85. 

Gay  Lussac's  Law  and  Pfeffer's  results,  84. 

Gay  Lussac's  Law  for  dilute  solutions,  84. 

Gibbs,  application  of  thermodynamics  to 
chemical  equilibrium,  64. 

Gladstone  and  Dale,  refraction  formula, 

I?- 
Goodwin  and  Thompson,  the  dielectric 

constant  of  liquid  ammonia,  211. 
Graham,  work  on  diffusion,  30. 
Grotthuss,  theory  of  electrolysis,  46. 
Guldberg    and    Waage,    law    of    mass 

action,  60. 
Guye,  hypothesis  of,  26. 

Hantzsch  and  Werner,  stereochemistry 
of  nitrogen,  27. 

Heat  of  combustion,  and  composition 
and  constitution,  37. 

Heat  of  neutralization  in  dilute  solutions, 
119. 

Heat  of  neutralization  of  acids  and  bases, 
a  constant,  36. 

Hess,  G.  H.,  work  of,  32. 

Hess's  law  of  thermoneutrality  of  salts,  33. 

Hess's  law  of  thermoneutrality  of  salt  so- 
lutions, 122. 

History  of  van't  HofF s  laws,  76. 

Hittorf,  work  on  migration  velocity  of 
ions,  52. 

Horstmann,  application  of  thermody- 
namics to  chemistry,  64. 

Hydrochloric  acid,  dry,  does  not  decom- 
pose carbonates,  163. 

Hydrochloric  acid,  dry,  doas  not  precipi- 
tate silver  nitrate  in  ether  or  benzene, 

165- 
Hydrochloric  acid,  dry,  no  action  on  dry 

ammonia,  168. 
Hydrogen  sulphide,  dry,  inactivity  of,  165. 

Indicators,  theory  of,  112. 

Ion  formation,  modes  of,  189. 

Ions,    experiment    to    demonstrate    the 

presence  of,  137. 

Ions  the  cause  of  chemical  reaction,  158. 
Ions,  velocity  of,  191. 

Jones  and  Allen,  experiment  to  demon- 
strate the  dissociating  action  of  water, 
113. 


Jones'  measurement  of  dissociation  by 
freezing-point  lowering,  compared  with 
dissociation  from  conductivity,  130. 

Jones,  measurement  of  dissociation  by 
the  boiling-point  method,  213. 

Kohlrausch's  Law  of  independent  migra- 
tion velocity  of  ions,  197. 

Kohlrausch,  on  conductivity  of  solutions, 
52. 

Kopp's  work  on  atomic  volumes,  12. 

Kopp's  work  on  boiling-points  of  liquids. 
4- 

Law  of  Avogadro,  for  dilute  solutions, 
87. 

Law  of  Faraday,  44. 

Law  of  Hess,  122. 

Law  of  Kohlrausch,  116. 

Law  of  mass  action,  Guldberg  and 
Waage,  60. 

Law  of  reaction  velocity,  discovery  of,  56, 

Laws  of  Boyle  and  Gay  Lussac,  applied 
to  solutions,  82. 

Laws  of  Boyle,  Gay  Lussac,  and  Avo- 
gadro for  solutions  and  gases,  general 
expression  of,  89. 

Laws  of  gas  pressure  not  always  applica- 
ble to  osmotic  pressure,  91. 

Le  Bel's  hypothesis,  23. 

Liquid  elements,  247 ;  theory  of,  247. 

Lodge,  experiment  on  absolute  velocity 
of  ions,  199. 

Lorenz-Lorentz,  refraction  formula,  17. 

Lessen,  on  molecular  volume,  13. 

Lowering  of  freezing-point  and  conduc- 
tivity, relation  between,  129. 

Lowering  of  freezing-point,  and  osmotic 
pressure,  relation  between,  126,  131. 

Lowering  of  freezing-point  and  rise  in 
boiling-point,  129. 

Lowering  of  vapor-tension  and  osmotic 
pressure,  relation  between,  127. 

Magnetic  rotation  and  composition  and 
constitution,  28. 

Magnetic  rotation  of  plane  of  polariza- 
tion, 27. 

Marignac,  specific  heat  of  aqueous  solu- 
tions, ii. 

Measurement  of  conductivity,  206. 


288 


INDEX 


Metamerism  and  properties,  2. 

Mixtures  of  completely  dissociated  com- 
pounds, 117. 

Mixtures  of  completely  undissociated 
compounds,  118. 

Molecular  conductivity,  203. 

Molecular  heats  and  composition,  8. 

Molecular  heats  and  constitution,  9. 

Molecular  rotatory  power,  22. 

Molecular  volume  and  composition,  n. 

Molecular  volumes,  n. 

Molecular    volumes    and    constitution, 


Nerhst  and  Ostwald,  experiment  to  de- 
monstrate free  ions,  139. 

Nernst,  calculation  of  electromotive  force, 
from  osmotic  pressure,  227. 

Nernst,  effect  of  an  access  of  one  of  the 
ions,  on  dissociation,  149. 

Neutralization,  change  of  volume  in,  107. 

Neutralization,  heat  of,  in  dilute  solu- 
tions, 119. 

Neutralization  of  acids  and  bases,  con- 
stant heat  of,  36. 

Noyes,  dissociation  measured  by  change 
in  solubility,  151. 

Optical  activity  and  composition  and 
constitution,  23. 

Optically  inactive  and  optically  active 
substances,  22. 

Origin  of  the  theory  of  electrolytic  dis- 
sociation, 71. 

Osmotic  investigations  of  Pfeffer,  71. 

Osmotic  pressure  and  conductivity,  re- 
lations between,  128. 

Osmotic  pressure  and  gas  pressure,  re- 
lations between,  76. 

Osmotic  pressure  and  lowering  of  freez- 
ing-point, relations  between,  126,  131. 

Osmotic  pressure  and  lowering  of  vapor- 
tension,  relations  between,  127,  134. 

Osmotic  pressure,  electromotive  force 
calculated  from,  227. 

Osmotic  pressure,  results  of  Pfeffer,  75. 

Ostwald  and  Nernst,  experiment  to  de- 
monstrate the  presence  of  free  ions, 

139- 

Ostwald,  change  in  volume  in  neutral- 
ization, 107. 


Ostwald,  dilution  law,  143. 

Ostwald,  method  of  measuring  affinity, 

67. 
Oxygen, "inactivity  of  dry,  162. 

Pean  de  St.  Gilles,  work  of,  58. 

Perkin,  W.  H.,  work  on  magnetic  rota- 
tion, 28. 

Pfeffer's  apparatus  for  measuring  osmotic 
pressure,  73. 

Pfeffer's  method  of  measuring  osmotic 
pressure,  72. 

Pfeffer's  osmotic  pressure  results,  75. 

Phenols,  toxic  action  of,  and  their  dis- 
sociation, 272. 

Physical  problem,  electrolytic  dissocia- 
tion applied  to,  226. 

Physiology,  animal,  application  of  physi- 
cal chemical  methods  to,  278. 

Physiology,  animal,  application  of  the 
dissociation  theory  to,  276. 

Polarized  light,  rotation  of  plane  of,  21. 

Potential  difference  between  metal  and 
solution,  236. 

Potential,  sources  of,  in  concentration 
element,  252. 

Raoult,  on  freezing-point  lowering  and 
lowering  of  vapor-tension,  30. 

Refraction  of  light,  16. 

Refraction  values  of  the  elements,  20. 

Refractive  power  of  salt  solutions,  specific, 
108. 

Rise  in  boiling-point,  and  osmotic  press- 
ure, relation  between,  127. 

Rodger  and  Thorpe,  on  viscosity,  14. 

Rose,  work  of,  55. 

Rotation  of  plane  of  polarized  light,  21. 

Rotatory  power  of  salt  solutions,  no. 

Rudolphi's  dilution  law,  147. 

Salt  solutions,  properties  are  additive, 
105. 

Schiff,  specific  heat  and  composition, 
10. 

Schorlemmer,  boiling-point  results,  6. 

Secretion,  application  of  osmotic  press- 
ure and  dissociation  to,  281. 

Semipermeable  membranes,  72. 

Silbermann  and  Favre,  thermochemical 
work,  33. 


INDEX 


289 


Solubility,  change  in,  as  a  measure  of 

dissociation,  151. 
Solutions  and   electrolytic   dissociation, 

172. 

Solutions,  the  study  of,  30. 
Solution-tension,  constancy  of,  236. 
Solution-tension,  electrolytic  231. 
Solvents,  different  dissociating  power  of, 

160. 

Soret,  principle  of,  86. 
Specific  conductivity,  202. 
Specific  gravity  of  salt  solutions,  105. 
Specific  heats  of  liquids,  8. 
Specific  refractive  power  of  salt  solutions, 

108. 

Stereochemistry  of  carbon,  23. 
Stereochemistry  of  nitrogen,  27. 
Stohmann,  thermochemical  work  of,  36. 
Strength  of  acids  and  bases,  216. 
Sulphuric  acid,  dry,  no  action  on  dry 

metallic  sodium,  169. 

Temperature  and  osmotic  pressure,  76. 
Temperatures,  conductivity  at  high,  215. 
Theories  of  electrolysis,  Grotthuss,  Clau- 

sius,  and  Williamson,  46. 
Thermochemical  results,  36. 
Thermochemistry,  the  development  of, 

32- 

Thermodynamics  applied  to  chemistry, 
64. 

Thomsen,  J.,  method  of  measuring  affin- 
ity, 67. 

Thomsen,  J.,  thermochemical  work  of,  35. 

Thomson,  J.  J.,  overthrows  argument 
against  the  Berzelius  chemical  theory, 
42. 

Thomson's,  J.  J.,  theory,  213. 


Thorpe  and  Rodger  on  viscosity,  14. 

Thorpe's  work  on  molecular  volumes,  13. 

Toxic  action  and  electrolytic  dissocia- 
tion, 268. 

Toxic  action  of  phenols  and  their  disso- 
ciation, 272. 

Toxic  action  of  substances  on  fungi,  275. 

Valson's  "  moduli,"  107. 

Van't  Hoff's  coefficient  " i"  calculation 
of,  96. 

Van't  Hoff's  coefficient  "z"  from  freez- 
ing-point lowering  and  conductivity, 
98. 

Van't  Hoff's  Laws,  history  of,  76. 

Van't  Hoff's  Lecture,  77. 

Van't  Hoff,  the  asymmetric  carbon  atom, 

23- 

Van't  Hoff,  velocity  of  reactions,  65. 
Vapor-tension,  lowering  of,  178. 
Vapor-tension,  lowering  of,  and  osmotic 

pressure,  relation  between,  134. 
Velocity,  absolute,  of  ions,  198. 
Velocity  of  ions,  Hittorf,  52. 
Velocity  of  ions,  191. 
Velocity,  relative,  of  ions,  192. 
Viscosity,  14. 

Water,  conductivity  of,  207. 

Water,  r61e  of,  in  chemical  activity,  160. 

Wenzel,  work  of,  53. 

Whetham,  experiment  on  absolute  veloc- 
ity of  ions,  199. 

Williamson,  theory  of  solution,  50. 

Wislicenus,  application  and  extension  of 
van't  Hoff's  hypothesis  of  the  asym- 
metric carbon  atom,  25. 

Wiillner,  lowering  of  vapor-pressure,  31. 


THE   STORAGE  BATTERY 


BY 
AUGUSTUS  TREADWELL,  Jr. 

E.  E.,  Associate  Member  A,  I.  E,  E. 

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THE  PRINCIPLES  OF  THE 
TRANSFORMER. 


By  FREDERICK  BEDELL,  Ph.D., 

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CONSTANT  CURRENT  TRANSFORMER. 


CONSTANT  POTENTIAL  TRANSFORMER. 

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